PUNJAB COLLEGE OF TECHNICAL EDUCATION, LUDHIANA COURSE BREAK UP 2010

Name of Instructor: Mr. Swapan Chanana Subject Name:BusinessMathematics Ms.NidhiVerma, Ms. Prabhjot Arora Subject Code: BB102Total No. of Lectures: 63

Course Information

This mathematics course emphasizes the mathematics required in general business processes. This course is designed to prepare students for the mathematical and analytical application required in subsequent business and economics courses.

This course covers those topics which can be used in day to day business transactions ,and covers the mathematical processes and techniques currently used in the fields of business and finance.

Learning outcome

Analysis of the Quantifiable data would help the students in interpreting better results. It is of great help to Judge Company’s performance.

Mathematics is an aid to decision making. For instance, Permutations & Combinations helps us in selecting the best alternative out of many.

It helps in deriving the relationship between two or more variables. Its practical application comes when the company wants to know the key variables involved in its success. For example, when we want to know whether the increase in profit is because of increase in sales or decrease in cost, we can use the principles of differentiation and maxima & minima. So, it is of great help in developing relationship between the variables.

They will be able to judge the growth of a company. A.P. & G.P. give an idea about the consistency in profit growth of a company.

Course topics

Linear & Quadratic Equations Matrix Algebra Permutations & Combinations Binomial Theorem Functions, Limits & Continuity Differential Calculus Arithmetic & Geometric Progressions

Logarithms Set Theory Real Number System Logical Statements & Truth Tables

Textbooks

Business Mathematics By DC Sancheti & VK Kapoor Spectrum Business Mathematics By Sharma & Sharma

Break up of Internal Assessment

BREAK UP WEIGHTAGE

MSE’s 15Presentation 5Assignments (3) 5 Tests (2) 10 CLASS TESTS (3) 5TOTAL 40

Punctuality

Assignments that are late will not be accepted and in case of an unavoidable circumstances, prior submission of the assignment is acceptable

LECTURE NO.

TOPIC TEST ASSGN

1,2 Chapter : Matrix AlgebraConcepts- Introduction- Order, representation, elements, diagonal of a matrix, Types of Matrices- Operations on matrices : addition, subtraction, multiplication

3 Examples- Ques on formation of matrices, operations, etc.

4,5 Concepts- Transpose- Determinant- Minors, Cofactors

- Adjoint- Inverse

6 Examples- Ques on dets, adj, etc.

7 Concepts- Cramers Rule- Special Cases

8 Concepts- Matrix Inversion Method- Special Cases

9.10 Concepts- Elementary Transformations- Gauss Elimination Method- Gauss Jordan Elimination Method

1

11 Chapter: Binomial TheoremConcepts- Introduction : coefficients, terms, no of terms- Binomial Theorem

12 - Intro contdExamples- Simple ex. on binomial expansion

13,14 - Middle terms- General term

15 - B. Thm with any Index- Examples

16&17 - Applications of B. thm18 Chapter : Set Theory

- Definition of a set- Methods of describing a set- Operations on sets

19 - Venn Diagrams (in brief)- Laws of Operation : Demorgan’s Laws, Distributive Laws, Associative Law

20 - Relations & Functions21 Chapter: Functions, Limits & Continuity

Concepts- Functions- Mappings

22 - Types of Functions- Limit of a function

23,24&25 Examples- Methods of evaluating limit of a function- Some important limits- Continuity of a function

26,27,28 Chapter: Differential Calculus

- Introduction- Basic Formulae- Sum Rule- Product Rule

29,30.31 - Quotient Rule- Problems- Chain Rule- Logarithmic Diff

32,33 - Diff by Substitution- Implicit Diff- Derivative of a function wrt another function

34,35 Concepts- Maxima & Minima- Points of Inflexion

36,37 Chapter: Logarithms- Introduction- Laws of Operations- Change of base

38,39 - Logarithm Tables- Operations with Logarithms

40 - Compound Interest 241 Chapter: Logical Statements & Truth

Tables- Introduction- Logical Statements- Truth tables- Negation

42,43 - Tautologies & Fallacies Propositions- Conditional Statements- Biconditional Statements

44 Chapter : Arithmetic & Geometric Progressions- Introduction- A.P., Sum of terms in A.P.- Questions for practice

45,46 - Representation of terms in A.P.- Arithmetic Mean- Problems

47,48,49 - Geometric Progression- Sum of a Series in G.P.- Geometric Mean

50 Chapter : Permutations & CombinationsConcepts- Introduction : perms, combs- Factorial

- Fundamental Rules of Counting51.52 Examples

- Questions on Counting principleConcepts- Permutations- Per of n Different things

53 - Circular Permutations- Perms of Things not all DifferentExamples- Ques on perms

54&55 Concepts- Combinations- Combs of things not all Different- Problems

3

56 Chapter : Real Number System- Number Systems, Natural Numbers- Integers, Prime Numbers, Rational & Irrational Numbers, Modulo

57,58 Chapter : Linear & Quadratic EquationsConcepts- Introduction- Degree of an equation: linear, quad, cubic, etc.- Solns to quad eqns : method of factorization- Simultaneous eqns- Method of factorization

59,60 Examples- Equations reducible to q.e.- Irrational eqs- Reciprocal Eqns

61,62 Concepts- Nature of roots- Symm expressions- Formation of an eq

63 PROBLEMS & REVISION

PRESENTATION:

There will be one presentation for the subject. The students will be divided into different groups. Each group consists of 2 members and will work upon a topic and present it.

TOPICS:

1. Degree of an equation2. Solution of a Quadratic Equation3. Nature of roots of a Quadratic Equation4. Formation of a Quadratic Equation5. Operations on Matrices6. Matrix Multiplication7. Determinant of a Matrix8. Inverse of a Matrix9. Cramer’s Rule10. Matrix Inversion Method11. Gauss Elimination Method12. Types of Matrices13. Fundamental Principle of Counting14. Difference between Permutations & Combinations15. Binomial Theorem16. Applications of Binomial Theorem17. Functions18. Limit of a function19. Product Rule & Quotient Rule20. Chain Rule & Parametric Differentiation21. Logarithmic Diff & Derivative of Function of a Function22. Maxima & Minima of a function23. A.P. Series24. G.P. Series25. Basic Operations on Logs26. Learning Log Tables27. Compound Interest and Depreciation

ASSIGNMENTS

Assignment no.1Topics: Matrix Algebra

1. Minor of 10 in the det

2. Solve the equations x + y + z = 7x + 2y + 3z = 16x + 3y + 4z = 22

by Gauss- Elimination method.

3. Solve the equations x – 2y + 3z = 42x + y – 3z = 5-x + y + 2z = 3

by Cramer’s rule.

4. State Cramer’s rule.5. Define Gauss Elimination Method.6. Define the inverse of a square matrix.

7. Find the inverse of the matrix

8. Solve by matrix inversion method:3x + y + 2z = 32x – 3y – z = -3x – 2y + z = 4

9. Solve by Cramer’s rule:x + 2y + z = 4-x + y + z = 0x – 3y + z = 2

10. Define a diagonal matrix and a unit matrix

Assignment no.2

Topics: Differential Calculus Logarithms

1. If , then find .

2. If find x.

3. Differentiate with respect to x, the function

4. If show that .

5. What is the function of log tables?6. Find the maximum and minimum values of .

7. If find .

8. Show that

9. Using logarithms, find the value of .

10. Show that

Assignment no.3

Logical Statements&Truth Tables, A.P. & G.P and Permutations & Combinations

1. Simplify .2. Prove that .3. How many numbers are there between 100 and 1000 such that every digit is either 2 or 3?4. Construct the truth table for the statement .5. In how many ways, the letters of the word ‘RAM’ can be arranged?6. Show that is a tautology.7. How many different committees can be formed consisting of 4 men & 3 women out

of 7 men & 5 women?8. Show that , where p, q are logical statements.9. What do you mean by permutations?10. Find the value of .

11. Find the sum of the series 72 + 70 + 60 + …… + 4012. If a, b, c are the and terms of a G.P., then prove that

13. Find the sum of 50 terms of the seqn. 7, 7.7, 7.77, 7.777,……..14. If the mth term of an A.P. is 1/n and nth term is 1/m, then show that the mnth term

is 1.

Practice Problems on Real Number System and Set Theory

1. Define complement of a set A ( ).2. Define Union & Intersection of two sets A and B.3. Find the nth term of the series 1 + 3 + 5 + 7 + 9 + ……4. If then show that .

5. Prove that is an irrational number.

Practice Problems on Linear & Quadratic Equations

1. Solve = 2

2. Solve

3. In a linear equation y = mx+c, what is meant by the terms m and c?4. Solve

5. Solve

6. Solve the equation 7. If α, β are the roots of the equation such that α, β are non zero,

α > β and then find the value of .

8. Solve the equation

9. What is the difference between linear and quadratic equations?10. Solve the following equation:

Practice Problems on Binomial Theorem and Functions, Limits & Continuity

1. Find the term independent of x in .

2. If f(x) = k, then find f(1) ( here k is a constant).

3. Evaluate .

4. Prove that the function is continuous at x = 1.5. What is Binomial Theorem? Explain its utility with suitable illustrations.6. Prove that the coefficient of xn in (1+x)2n is twice the coefficient of xn in

(1+x)2n-1.

7. Find the third term from the end in the expansion of .

8. A function f is defined as

Show that f(x) is differentiable at x=1 and find its value.

9. Evaluate .

10. Prove that the function is discontinuous at x=3.