INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA

COURSE OUTLINE

KulliyyahEngineering

DepartmentScience in Engineering

ProgrammeAll Programmes

Course TitleEngineering Calculus II

Course CodeMTH 1212

StatusCore

Level1

Credit Hours

3

Contact Hours3

Pre-requisites

(if any)MTH 1112

Co-requisites

(if any)-

Instructor(s)

Semester OfferedEvery Semester

Course

SynopsisParametric equations and polar coordinates, vectors and geometry in space, multivariable functions, partial derivatives and multiple integrals with applications, vector valued functions, vector calculus.

Course ObjectivesThe objectives of this course are to:

1. Help students deeply understand the definitions and the concept of calculus with emphasis on parametric equations, polar coordinates and vectors with more realistic applications.

2. Expose the elementary theory of calculus for multivariable functions and its applications in differentiation and integration.

3. Enable students think multidimensional through understanding different coordinate systems.

4. Familiarize students with vector calculus and its application in engineering.

5. To enhance the useful of calculus through the mathematical models of daily life engineering applications.

Learning OutcomesUpon completing this course, students should be able to:

1. Use parametric equations in Cartesian and polar form in defining curves, conics and evaluating tangents, areas and arc length.2. Extend the notion and properties of vectors in R3 and apply vectors to describe and sketch level curves, lines, planes and surfaces.3. Apply the concept of limit and continuity in computing limit and determining the continuity of a function of several variables.

4. Understand the concept and computing techniques of partial derivatives with applications such as, tangent planes, linear approximations, directional derivatives, gradient vector and optimization.5. Evaluate double and triple integrals using Cartesian, polar, cylindrical and spherical coordinate systems.

6. Apply curve parameterization, potential function, conservative vector field and independence of path to evaluate line and surface integrals.

7. Determine the gradient, divergence and curl of vector fields and apply Greens, Gauss divergence and Stokes theorems.

Instructional

StrategiesLectures and Tutorials

Course Assessment

State weightage of each type of assessment.

LO

Method

Percentage

1-6

Quizzes

151-7

Assignments

151-3

Mid-term Examination (s)

301-7

Final Examination

40

Content Outlines

WeeksTopicsTask/Reading

1-2Parametric Equations and Polar Co-ordinatesCurves defined by parametric equations, tangents, areas, arc length and surface area, curves defined by polar coordinate, tangents, areas, and lengths in polar coordinates, conic sections.Chapter 9

3-4Vectors and Geometry in SpaceVectors in plane and space, dot product and cross product, lines and planes in space, quadric surfacesChapter

10

5Function of Several VariablesFunctions of two variables, domain and range, graphs, level curves, functions of three or more variables.Chapter

12

6-7Partial Derivatives

Limits and continuity, partial derivatives, higher derivatives, tangent plane and linear approximations, differentials, chain rule, directional derivatives and the gradient vector.Chapter

12

8Maximum and Minimum ValuesLocal extrema, global extrema, Lagrange multipliers.Chapter

12

9-10Multiple Integrals

Double integrals over rectangle, iterated integrals, double integrals over general regions, area, volume, mass, centre of mass, double integrals in polar coordinates, surface area, triple integrals, triple integrals in cylindrical and spherical coordinates, change of variables in multiple integral and Jacobian.Chapter

13

11-12Vector Valued FunctionsDefinition, continuity, limits, derivative and integral of vector valued functions, velocity, curvature, tangent and normal vectors, velocity, acceleration.Chapter

11

13-14Vector CalculusScalar, vector and gradient fields, potential function, line integral, curl and divergence, Greens, Stokes and Gauss divergence theorem, surface integrals.Chapter

14

ReferencesRequired:

Robert, T.S. & Roland, B.M. (2006). Calculus (3rd ed.). McGraw- Hill.

Recommended:

1. Anton, H., Bivens, I. & Davis, S. (2002). Calculus (7th ed.). John Wiley.

2. Edwards, C.H. & Penny, D.E. (2002). Calculus (6th ed.). Prentice Hall.

3. Finney, R.L., & Weir, M.D.L.F., & Giordano. (2001). Thomas Calculus (10th ed.). Addison-Wesley Publishing Company.

4. Johnston, E.H., & Mathews, J.C. (2002). Calculus(1st ed.). Addison Wesley.

5. Stewart, J. (2003). Calculus (5th ed.). Brooks/Cole-Thomson Learning.

6. Strauss, M.J., Bradley, G.L. & Smith, K.J. (2002). Calculus (3rd ed.). Prentice Hall.

Proposed Start Date (Semester)Semester II, 2009/2010

Batch of Students to be AffectedSemester II, 2009/2010 and onward

Prepared by:

Dr Jamal I. Daoud Assistant ProfessorKulliyyah of Engineeing

Checked by:

Dr Jamal I. Daoud Head of DepartmentKulliyyah of Engineeing

Approved by:

Dr Amir Akramin Shafie Dean Kulliyyah of Engineeing

Learning Outcomes Matrix: MTH 1212 / Engineering Calculus II Course Learning OutcomesProgramme Outcomes

Outcome 1Outcome 2

Outcome 3Outcome 4Outcome 5Outcome 6

Outcome 7

Outcome 8Outcome 9Outcome 10

Outcome 11Outcome 12

1. Use parametric equations in Cartesian and polar form in defining curves, conics and evaluating tangents, areas and arc length.3121

2. Extend the notion and properties of vectors in R3 and apply vectors to describe and sketch level curves, lines, planes and surfaces.3121

3. Apply the concept of limit and continuity in computing limit and determining the continuity of a function of several variables.3121

4. Understand the concept of partial derivatives and computing techniques with application such as, tangent planes, linear approximations, directional derivatives, gradient vector and optimization.3121

5. Evaluate double and triple integrals using Cartesian, polar, cylindrical and spherical coordinate systems.3121

6. Apply curve parameterization, potential function, conservative vector field and independence of path to evaluate line and surface integrals.3121

7. Determine the gradient, divergence and curl of vector fields and apply Greens, Gauss divergence and Stokes theorems.3121

Total217147

*1 = objective addresses outcome slightly,2 = moderately,3 =substantive

The educational outcomes of the programmes conducted by the Kulliyyah are as follows:1. The ability to acquire and apply knowledge of mathematics, computers, science, and engineering.(T)

2. The ability to have in-depth understanding and technical competency in relevant engineering discipline. (T)

3. The ability to identify, formulate and provide solutions to engineering problems. (T)

4. The ability to design and conduct experiments, as well as to analyze and interpret data. .(A/D)

5. The ability to analyze and design a system, component, or process to achieve the required objectives.( A/D)

6. The ability to understand and apply design principles for sustainable development. ( A/D)

7. The ability to communicate effectively.(S)

8. The ability to function effectively as an individual and in group with the capacity to be a leader or manager as well as an effective team member.(S)

9. The ability to recognize the need for lifelong learning and to pursue independent learning for professional development.(S)

10. The ability to understand the responsibility of a professional engineer in the context of contemporary social, cultural, global and environmental issues.(ESSE)

11. The ability to demonstrate understanding and commitment to professional and ethical responsibilities.(ESSE)

12. The ability to understand the impact of engineering solutions in a global and societal context through broad-based education.(ESSE)