PMAT 12203: Introduction to Calculus

Course code   : PMAT 12203

Title                  : Introduction to Calculus

 Learning Outcomes:

At the end of this course, the student should be able to

1. define the basic concepts of limits
2. evaluate the limits of functions
3. find rates of change
4. recognize the continuity of a function
5. explain basic rules of differentiation
6. identify indeterminate forms and methods of integration
7. define an ordinary differential equation
8. solve applications related to the ordinary differential equations appear in biology

Course Contents:

Limits and Derivatives: 

• Intuitive definition of a limit, one sided limits, Calculating limits using limit laws, Derivatives and Rates of change, Derivative as a function
  
  

Continuity:

• Continuity at a point, continuity on an interval, Intermediate value theorem
  
  

Differentiation Rules: 

• Derivatives of polynomials and Exponential functions, Product and quotient rules, Derivatives of Trigonometric functions, Chain rule, Implicit differentiation, Derivatives of Logarithmic functions
  
  

Applications of Differentiation:

• Maximum and Minimum values, Indeterminate forms and l’Hospital’s rule, Taylor's formula, Newton's method

Techniques of Integration:

• Basic integrals, Integration by parts, Trigonometric integrals, Trigonometric substitution, Integration of rational functions by partial fractions, Improper integrals

Introduction to Differential Equations: 

• Separable equations, Linear equations, Applications related to biology

Method of Teaching and Learning : A combination of lectures and tutorial discussions.

Assessment : Based on the tutorials, tests, and end of course examination.

Recommended reading: 

1. Ayres, Jr .F. & Mendelson, E., (6th edition, 2012). Schaum's Outline of Calculus, McGraw-Hill.

2. Arora, S. & Malik, S.C., (5th edition, 2017). Mathematical Analysis, New Age International.

3. Stewart, J., Clegg, D.K., & Watson, S. (11th Ed., 2020). Calculus: early transcendentals. Cengage
   Learning.