At the end of the course, the students will be able to:
Solve problems of Calculus, Laplace Transformation and Fourier Series, and develop mathematical skills and logical perceptions in the use of mathematical instruments.

1. FUNCTIONS & LIMITS.                                                                6 hours
1.1 Constant & Variable Quantities
1.2 Functions & their classification
1.3 The concept of Limit
1.4 Limit of a Function
1.5 Fundamental Theorems on Limit
1.6 Some important Limits
1.7 Problems
2. DIFFERENTIATION                                                                         6 hours
2.1 Increments
2.2 Differential Coefficient or Derivative
2.3 Differentiation ab-initio or by first Principle
2.4 Geometrical Interpretation of Differential Coefficient
2.5 Differential Coefficient of Xn
and (ax + b)n
2.6 Three important rules
2.7 Problems
3. DIFFERENTIATION OF ALGEBRAIC FUNCTIONS                         9 hours
3.1 Explicit Functions
3.2 Implicit Functions
3.3 Parametric forms
3.4 Problems
4. DIFFERENTIATION OF TRIGONOMETRIC FUNCTIONS                6 hours
4.1 Differential Coefficient of Sin x, Cos x, Tan x from first principle.
4.2 Differential Coefficient of Cosec x, Sec x, Cot x
4.3 Differential Coefficient of Inverse trigonometric functions.
4.4 Problems.

5. DIFFERENTIATION OF LOGARITHMIC & EXPONENTIAL FUNCTIONS                                                                                                                         6 hours
5.1 Differentiation of ln x
5.2 Differentiation of Log ax
5.3 Differentiation of a

5.4 Differentiation of ex
5.5 Problems
6. RATE OF CHANGE OF VARIABLES                                            6 hours
6.1 Increasing and decreasing functions
6.2 Maxima and Minima
6.3 Criteria for maximum & minimum values
6.4 Methods of finding maximum & minimum
6.5 Rate measure
6.6 Slope of a line
6.7 Velocity and acceleration
6.8 Problems
7. INTEGRATION(SIMPLE BASIC RULES)                                        9 hours
7.1 Concept
7.2 Fundamental Formulas
7.3 Important Rules
7.4 Problems
8. METHODS OF INTEGRATION                                                         9 hours
8.1 Integration by substitution
8.2 Integration by parts
8.3 Problems
9. DEFINITE INTEGRALS                                                                     6 hours
9.1 Properties
9.2 Application to area
9.3 Problems
10. DIFFERENTIAL EQUATIONS                                                         6 hours
10.1 Introduction
10.2 Order and Degree
10.3 First order Differential Equation of Ist degree.
10.4 Solution of problems
10.5 Problems
11. LAPLACE TRANSFORMATIONS                                                   9 hours
11.1 Laplace Transformations
11.2 Inverse Laplace Transformations
11.3 Problems.
12. FOURIER SERIES.                                                                          9 hours
12.1 Introduction
12.2 Periodic Functions
12.3 Even and Odd Functions
12.4 Problems
13. STATISTICS                                                                                     9 hours
13.1 Concept of mean, median and mode
13.2 Standard Deviation
13.3 Laws of probability

13.4 Problems

RECOMMENDED BOOKS
1. Thomas Finny, Calculus and Analytic Geometry
2. Ghulam Yasin Minhas, Technical Mathematics Vol – I & II, Ilmi Kitab Khana, Lahore.
3. Riaz Ali Khan, Polytechnic Mathematic Series Vol I & II, Majeed Sons, Faisalabad
4. Sana Ullah Bhatti, Calculus and Analytic Geometry, Punjab Text Book Board, Lahore.