Brief Teaching Plan Math30202 Calculus Term 2 …math/course/2557/S2/MATH30202/brief calc plan2_57… · Brief Teaching Plan Math30202 Calculus Term 2 Academic year 2014 - 1 -

Brief Teaching Plan Math30202 Calculus Term 2 Academic year 2014 - 1 -

Brief Teaching and Evaluation Plan Course MATH30202 (Calculus) 1.5 credits 3 period/week Grade Level 11 Term 2 Academic year 2014 Instructors 1. Nakorn Junla 2. Deaw Jaibun 3. Jongsool Choi 1. Course Description

This course will familiarize students with limits and continuity of functions, derivatives, integrals, applications of integration, techniques of integration, improper integrals, sequences and series, infinite series including Maclaurin and Taylor series; power series, and approximating functions by Taylor polynomials.

2. Expected learning outcomes By the end of this course, students should be able to 1. analyze and evaluate limits of given functions 2. analyze functions for continuity 3. evaluate derivatives and integrals of functions 4. apply differentiation and integration techniques to solve mathematical problems 5. evaluate general terms and limits of given sequences 6. analyze the convergence of given infinite series 7. evaluate the infinite sum of given infinite series 8. evaluate and apply Taylor series around any given point to solve mathematical problems


3. Weekly tentative teaching plans and objectives

Weeks Periods Contents Objectives Instructional methods Instructional media

1 A 20-24 Oct 14

1-3

1.1 Limits (An intuitive approach) - Limits - One-sided limits - Infinite limits 1.2 Computing limits - Basic limits - Limits of polynomial and rational functions - Limits involving radicals - limits of piecewise-defined functions 1.3 Limits at infinity - Limits at infinity and horizontal asymptotes - Limit laws for limits at infinity - Infinite limits at infinity - Limits at infinity of polynomial and rational functions - Limits at infinity involving radicals 1.4 Limits (Formal definition)

Students should be able to 1. understand the concepts of limits, one-sided limits, and infinite limit 2. evaluate the limits of polynomial and rational functions 3. understand the concept and evaluate the limits at infinity and horizontal asymptote 4. use laws of limits at infinity to evaluate the limit of any given function. 5. understand the concept of the formal definition of limits

Deductive reasoning, problem solving, and creative thinking

Text book: Calculus (Howard Anton)

2 B 27-31 Oct 14

4-6

1.5 Continuity - Definition of continuity - Continuity in an interval - Properties of continuous functions

6. understand the concepts of continuity , continuity in an interval, and properties of continuous functions.





- The intermediate-value theorem 1.6 Continuity of trigonometric functions - Continuity of trigonometric functions - The squeezing theorem 2.1 Tangent lines and rates of change - Tangent lines - Velocity - Slopes and rates of change - Rates of change in applications 2.2 The derivative function - Definition of The derivative function - Computing instantaneous velocity - Differentiability - The relationship between differentiability and continuity - Derivatives at the endpoints of an interval

7. apply the intermediate-value theorem 8. understand the concept of continuity of trigonometric functions and apply squeezing theorem 9. understand the concepts of tangent lines, velocity, and rates of change 10. solve the problems relating to rates of change 11. understand the concepts of a derivative function and differentiability 12. understand the concept of derivatives at the endpoints of an interval

3 A 3-7 Nov 14

7-9

2.3 Introduction to techniques of differentiation - Derivatives of power functions - Derivatives of a constant times a function

13. use techniques of differentiation to evaluate derivatives of given functions 14. evaluate higher order of derivatives of given functions 15. evaluate derivatives of functions





- Derivatives of sums and differences - Higher derivatives 2.4 The product and quotient rules - Derivative of a product - Derivative of a quotient 2.5 Derivatives of trigonometric functions

using product and quotient rules 16. evaluate derivatives of trigonometric functions

4 B 10-14 Nov 14

10-12

2.6 The chain rule - Derivatives of compositions - An alternative version of the chain rule - Generalized derivative formulas 2.7 Implicit differentiation - Functions defined explicitly and implicitly - Implicit differentiation 2.8 Related rates 2.9 Local linear approximation; Differentials - Differentials - Local linear approximation from the differential point of view

17. understand the concept of the chain rule and use it to evaluate derivatives of functions 18. understand the concept of implicit differentiation and solve problems relating to it 19. solve problems relating to related rates. 20. understand the concepts of the local linear approximation and differentials



5 A 17-21 Nov 14

13-15 3.1 Analysis of function I : Increase, decrease, and concavity

21. understand the concepts of increasing, decreasing, concavity and





- Increasing and decreasing functions - Concavity - Inflection points 3.2 Analysis of function I : Relative extrema ; Graphing polynomials - Relative maxima and minima - First derivative test - Second derivative test - Analysis of polynomials 3.3 Analysis of function II : Rational functions, cusps, and vertical tangents - Graphing rational functions

inflection points of functions 22. understand the concept of relative extrema 23. use the first and second derivative tests to analyze the behavior of the graphs of polynomial functions 24. sketch the graphs of rational functions using the concept of relative extrema, cusps, and vertical tangents

6 B 24-28 Nov 14

16-18

3.4 Absolute maxima and minima - Absolute extrema - The extreme value theorem - Absolute extrema on infinite intervals - Absolute extrma on open intervals 3.5 Applied maximum and minimum problems - Problems involving finite closed intervals - Problems involving intervals that are not both finite and closed 3.6 Rectilinear motion

25. understand the concepts of absolute extrema both on infinite intervals and open intervals 26. solve applied maximum and minimum problems 27. understand the concept of rectilinear motion





- Velocity and speed - Acceleration - Analyzing the position versus time curve

7 A 1-5 Dec 14

19-21

3.7 Newton’s method 3.8 Rolle’s theorem; Mean-value theorem 4.1 An overview of the area problem - The rectangle method for evaluateing areas - The antiderivative method for evaluateing areas 4.2 The Indefinite integral - Antiderivatives - The indefinite integral - Integration formulas - Properties of the indefinite integral

28. understand the concept of Newton’s method and use it to solve related problems 29. understand the concepts of the rectangle method and the antiderivative method for evaluateing areas 30. understanding the concept of the indefinite integral 31. use the integration formulas and properties of the indefinite integral to solve related problems



8 B 8-12 Dec 14

22-24

4.3 Integration by substitution 4.4 The definition of area as a limit; Sigma notation - Sigma notation - Properties of sums - Summation formulas

32. understand the concept of integration by substitution and use it to solve related problems 33. understand the concepts of area as a limit and the net signed area 34. understand the concepts of the





- A definition of area - Net signed area 4.5 The definite integral - Riemann sums and the definite integral - Properties of the definite integral - Discontinuity and integrability 4.6 The Fundamental theorem of calculus - The Fundamental theorem of calculus - The Mean-value theorem for integrals - Part 2 of the fundamental theorem of calculus - Integrating rates of change

definite integral and Riemann sums 35. us the properties of the definite integral to solve related problems 36. understand the concept of the fundamental theorem of calculus and apply it to solve related problems 37. apply the mean-value theorem for integrals to solves related problems

9 A 15-19 Dec 14

25-27

4.7 Rectilinear motion revisited using integration - Computing displacement and distance traveled by integration - Analyzing the velocity versus time curve - Constant acceleration 4.8 Average value of a function and its applications

38. understand the concept of rectilinear motion in term of integration 39. evaluate the average value of a function 40. evaluate definite integrals by substitution





- Average velocity revisited - Average value of a continuous function - Average value and average velocity 4.9 Evaluating definite integrals by substitution

22-26 Dec 14

Midterm

10 B 29-31 Dec14, 1-2 Jan 15

28-30

5.1 Area between two curves - Area between y = f(x) and y = g(x) 5.2 Volumes by slicing; Disks and washers - Volumes by slicing - Volumes by disks perpendicular to the x-axis - Volumes by washers perpendicular to the x-axis - Volumes by disks and washers perpendicular to the y-axis - Other axes of revolution 5.3 Volumes by cylindrical shells - Cylindrical shells - Variations of the method of cylindrical shells

41. evaluate the area between two curves 42. evaluate the volumes of revolution using disk and washer methods 43. apply the cylindrical shell method to evaluate the volume of revolution





11 A 5-9 Jan 15

31-33

5.4 Length of a plane curve - Arc length 5.5 Area of a surface of revolution - Surface area 5.6 Work - Work done by a variable force applied in the direction of motion 5.7 Moments, centers of gravity, and centroids - Density and mass of a lamina - Center of gravity of a lamina 5.8 Fluid pressure and force

44. evaluate the arc length of a given curve 45. evaluate the surface area of a given function 46. evaluate the work done by a variable force applied in the direction of motion 47. evaluate moments, centers of gravity, and centroids of a given lamina 48. understand the concept of fluid pressure and force



12 B 12-16 Jan 15

34-36

6.2 Derivatives and integrals involving logarithmic functions - Derivatives of logarithmic functions - Logarithmic differentiation 6.3 Derivatives of inverse functions; derivatives and integrals involving exponential functions - Differentiability of inverse functions - Derivatives of exponential functions - Integrals involving exponential functions 6.5 L’hopital’s rule; Indeterminate

49. evaluate derivatives of logarithmic and exponential functions 50. evaluate integrals of logarithmic and exponential functions 51. evaluate derivatives and integrals of inverse functions 52. use L’hopital’s rule to solve related problems 53. understand the concept of logarithmic and other functions defined by integrals 54. evaluate the derivatives and





forms - Indeterminate forms of types 0/0, ∞/∞, 0•∞, ∞-∞, 00, ∞0, and 1∞ 6.6 Logarithmic and other functions defined by integrals 6.7 Derivatives and integrals involving inverse trigonometric functions - Derivatives of the inverse trigonometric functions

integrals of inverse trigonometric functions

13 A 19-23 Jan 15

37-39

6.8 Hyperbolic functions and hanging cables - Definitions of hyperbolic functions - Hyperbolic identities - Derivative and integral formulas - Inverse of hyperbolic functions - Logarithmic forms of inverse hyperbolic functions - Derivatives and integrals involving inverse hyperbolic functions 7.1 An overview of integration methods 7.2 Integration by parts 7.3 Integrating trigonometric functions - Integrating powers of sine and cosine

55. understand the concept of hyperbolic functions 56. evaluate the derivatives and integrals of hyperbolic functions 57. use integration by parts to evaluate the integral of a given function 58. apply the concept of integrating trigonometric functions to solve related problems 59. use trigonometric substitutions to solve related problems





- Integrating products of sines and cosines - Integrating powers of tangent and secant - Integrating products of tangents and secants 7.4 Trigonometric substitutions - The method of trigonometric substitution

14 B 26-30 Jan 15

40-42

7.5 Integrating rational functions by partial fractions - Partial fractions - Linear factors - Quadratic factor 7.8 Improper integrals - Improper integrals - Integrals over infinite intervals - Integrals whose integrands have infinite discontinuities - Arc length and surface area using improper integrals

60. apply the integrating rational functions by partial fractions to solve related problems 61. understand the concept of improper integrals 62. use improper integral to solve related problems



15 A 2-6 Feb 15

43-45 9.1 Sequences - Definition of a sequence - Limit of a sequence

63. evaluate the limit of a given sequence 64. us the squeezing theorem for





- The squeezing theorem for sequence - sequences defined recursively 9.2 Monotone sequences - Testing for monotonicity - Convergence of monotone sequence 9.3 Infinite series - Sums of infinite series - Geometric series - Telescoping sums - Harmonic series

sequence to solve related problems 65. understand the concept of monotone sequences and their convergence 66. evaluate the sums of infinite series 67. understand the concepts of the geometric series, telescoping series, and harmonic series and apply them to evaluate the sums of given series

16 B 9-13 Feb 15

46-48

9.4 Convergence tests - The divergence test - Algebraic properties of infinite series - The integral test - p-series 9.5 The comparison, ratio, and root tests - The comparison test - The limit comparison test - The ratio test - The root test 9.6 Alternating series; Absolute and conditional convergence - Alternating series

68. apply the divergence test, the integral test, and the concept of p-series to test given series for convergence 69. apply the comparison, ratio, and root tests to test given series for convergence 70. understand the concepts of alternating series, absolute convergence, and conditional convergence 71. test the given series for absolute convergence





- Absolute convergence - Conditional convergence - The ratio test for absolute convergence 9.7 Maclaurin and Taylor polynomials - Maclaurin polynomials - Taylor polynomials - Sigma notation for Taylor and Maclaurin polynomials

17 A 23-27 Feb 15

49-51

9.8 Maclaurin and Taylor series; Power series - Maclaurin and Taylor series - Power series in x - Radius and interval of convergence - Power series in x – x0 - Functions defined by power series 9.9 Convergence of Taylor series - Approximating trigonometric functions - Approximating exponential and logarithmic functions - Binomial series - Some important Maclaurin series 9.10 Differentiating and integrating

72. understand the concept of Maclaurin and Taylor series 73. understand the concept of power series in x 74. evaluate radius and interval of convergence of given power series 75. approximate given functions using Taylor series 76. evaluate the derivatives and the integrals of given functions as power series *77. understand the concept of separation of variables *78. understand the concept of Euler’s method





power series; modeling with Taylor series - Differentiating power series - Integrating power series *8.1 Modeling with differential equations *8.2 Separation of variables - First-order separable equations - Exponential growth and decay models *8.3 Slope fields; Euler’s method *8.4 First-order differential equations and applications - First-order linear equations (* if time permit)

*79. use the concept of the first-order linear equation to solve related problems

2-6 Mar 15

Final


4. Evaluation and Grading 4.1 Assignments and homework 10 points 4.2 Student behavior 10 points 4.3 Quizzes (Pre-midterm and Post-midterm 10 points each) 20 points 4.4 Midterm exam 30 points 4.5 Final exam 30 points Total 100 points Evaluation and grading details 4.1 Assignments and homework (10 points)

Topic Work detail Assigned date Due date Time required Points 1. Limits and continuity Individual Week Week 60 mins 2 2. Derivative and applications Individual Week Week 60 mins 2 3. Integration and applications Individual Week Week 60 mins 2 4. Principles and techniques of integral evaluation Individual Week Week 60 mins 2 5. Infinite series Individual Week Week 60 mins 2

Total 300 mins 10

Not that Time required for students to do each assignment is based on the difficulty and length of a particular assignment.


4.2 Student behavior (affective domain) (10 points) Detail as in the following table.

Behavior

Evaluation Exceptional

good (5)

Very good (4)

Good (3)

Neutral (2)

Need improvement

(1)

1. Concentration in class

2. Punctuality in turning in assignment

3. Participation in class

4. Discipline

5. Responsibility

6. Initiative creativity

7. Ability to work with other students

8. Ability to manage time

9. Ability to solve Mathematical problems

10. Ability to be self-determined


4.3. Quizzes (20 points) There are two quizzes in this courses.

4.3.1 Pre-midterm quiz (90 mins) during 24-28 Nov 14 for 10 points. 4.3.2 Post-midterm quiz (90 mins) during 26-30 Jan 15 for 10 points.

Topics to be included in each quiz are shown in the following tables.

Topics The number of problems points Pre-midterm quiz : There are 8 problems which are required complete solutions.

1.

Limits, One-sided limit, Infinite limits, Limits of polynomial and rational functions, Limits involving radicals , limits of piecewise-defined functions, Limits at infinity, Limits at infinity of polynomial and rational functions, Limits at infinity involving radicals

2 2.5

2.

Definition of continuity, Continuity in an interval, Properties of continuous functions, The intermediate-value theorem, Continuity of trigonometric functions, Continuity of trigonometric functions, The squeezing theorem

2 2.5

3. Tangent lines, Velocity, Slopes and rates of change, Rates of change in applications, Definition of The derivative function, Computing instantaneous velocity, Differentiability, The relationship between differentiability and continuity, Derivatives at the endpoints of an interval, Derivatives of power functions, Derivatives of a constant times a function, Derivatives of sums and differences, Higher derivatives, The product and quotient rules, Derivatives of trigonometric functions, The chain rule, Implicit differentiation, Related rates, Local linear approximation, Differentials

4 5

Total 8 10


Topics The number of problems points Post-midterm quiz : There are 8 problems which are required complete solutions.

1. Area between y = f(x) and y = g(x), Volumes by slicing; Disks and washers, Volumes by cylindrical shells, Arc length, Surface area, Work, Moments, centers of gravity, and centroids, Derivatives and integrals involving logarithmic functions, Derivatives of inverse functions; derivatives and integrals involving exponential functions, L’hopital’s rule; Indeterminate forms

2

2.5

2. Logarithmic and other functions defined by integrals, Derivatives and integrals involving inverse trigonometric functions, Hyperbolic functions, Hyperbolic identities, Derivative and integral formulas, Inverse of hyperbolic functions, Logarithmic forms of inverse hyperbolic functions, Derivatives and integrals involving inverse hyperbolic functions

2

2.5

3. Integration by parts, Integrating trigonometric functions, Integrating powers of sine and cosine, Integrating products of sines and cosines, Integrating products of sines and cosines, Integrating powers of tangent and secant, Integrating products of tangents and secants, Trigonometric substitutions Integrating rational functions by partial fractions, Improper integrals

4

5

Total 8 10


4.4. Midterm exam (30 points) The midterm exam is set to be during 22-26 Dec 2014. It is a 100-minute exam of a total of 30 points. There are 8 problems which are required complete solutions. The topics to be included in the midterm exam are shown in the following table.

Topics The number of problems points 1. Limits, One-sided limit, Infinite limits, Limits of polynomial and rational functions, Limits involving radicals, limits of piecewise-defined functions, Limits at infinity, Limits at infinity of polynomial and rational functions, Limits at infinity involving radicals, Definition of continuity, Continuity in an interval, Properties of continuous functions, The intermediate-value theorem, Continuity of trigonometric functions, Continuity of trigonometric functions, The squeezing theorem, Tangent lines, Velocity, Slopes and rates of change, Rates of change in applications, Definition of The derivative function, Computing instantaneous velocity, Differentiability, The relationship between differentiability and continuity, Derivatives at the endpoints of an interval, Derivatives of power functions, Derivatives of a constant times a function, Derivatives of sums and differences, Higher derivatives, The product and quotient rules, Derivatives of trigonometric functions, The chain rule, Implicit differentiation, Related rates, Local linear approximation, Differentials, Tangent lines, Velocity, Slopes and rates of change, Rates of change in applications, The product and quotient rules, Derivatives of trigonometric functions, The chain rule, Implicit differentiation

2 10

2. Increase, decrease, and concavity, Inflection points, Relative extrema ; Graphing polynomials, First derivative test, Second derivative test, Rational functions, cusps, and vertical tangents, Graphing rational functions, Absolute maxima and minima, Applied maximum and minimum problems, Velocity and speed, Acceleration, Newton’s method, Rolle’s theorem; Mean-value theorem

2 10


3. The rectangle method for evaluateing areas, The antiderivative method for evaluateing areas, The Indefinite integral, Antiderivatives, Integration formulas, Properties of the indefinite integral, Integration by substitution, Evaluating definite integrals by substitution, The definition of area as a limit; Sigma notation, The definite integral, Riemann sums and the definite integralม Properties of the definite integral, Discontinuity and integrability, The

Fundamental theorem of calculus, The Mean-value theorem for integrals, Integrating rates of change, Computing displacement and distance traveled by integration, Analyzing the velocity versus time curve, Constant acceleration, Average value of a function and its applications, Average velocity revisited, Average value of a continuous function, Average value and average velocity

4

10

Total 8 30 4.5. Final exam (30 points)

The final exam is set to be during 2-6 Mar 2015. It is a 100-minute exam of a total of 30 points. There are 8 problems which are required complete solutions. The topics to be included in the midterm exam are shown in the following table.

Topics The number of problems points 1. Area between y = f(x) and y = g(x), Volumes by slicing; Disks and washers, Volumes by cylindrical shells, Derivatives and integrals involving logarithmic functions, Derivatives of inverse functions; derivatives and integrals involving exponential functions, Logarithmic and other functions defined by integrals, Derivatives and integrals involving inverse trigonometric functions, Integrating trigonometric functions, Integrating powers of sine and cosine, Integrating products of sines and cosines, Integrating products of sines and cosines, Integrating powers of tangent and secant, Integrating products of tangents and secants, Trigonometric substitutions, Integrating rational functions by partial fractions, Improper integrals

4 10


Topics The number of problems points 2. Sequences, Limit of a sequence, The squeezing theorem for sequence, sequences defined recursively, Monotone sequences, Convergence of monotone sequence, Infinite series, Sums of infinite series, Geometric series, Telescoping sums, Harmonic series, Convergence tests, The divergence test, Algebraic properties of infinite series, The integral test, p-series, The comparison, The limit comparison test, ratio, and root tests, Alternating series; Absolute and conditional convergence, Maclaurin and Taylor polynomials, Maclaurin and Taylor series; Power series, Radius and interval of convergence, Functions defined by power series, Convergence of Taylor series, Approximating trigonometric functions, Approximating exponential and logarithmic functions, Binomial series, Some important Maclaurin series, Differentiating and integrating power series; modeling with Taylor series

4

20

Total 8 30

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Brief Teaching Plan Math30202 Calculus Term 2 …math/course/2557/S2/MATH30202/brief calc plan2_57… · Brief Teaching Plan Math30202 Calculus Term 2 Academic year 2014 - 1 -