Course Description

M - 105 Differential Calculus

Real numbers, functions, Limits, continuity. Derivatives, differentials, chain rule, implicit differentiation. Higher order derivatives, local extrema, concavity, horizontal and vertical asymptotes, applications of extrema, related rates. Rolle's theorem, mean value theorem, inverse trigonometric functions. Conic sections.

Prerequisite:    NIL

Textbook(s)/ Required Material

Calculus by Edward and Penny  6^th Ed  (International Edition).

Course details:

1. Functions, Graphs, and Models.

Functions and Mathematical Modeling. Graphs of Equations and Functions. Polynomials and Algebraic Functions. Transcendental Functions. Preview: What Is Calculus?

2. Prelude to Calculus.

Tangent Lines and Slope Predictors. The Limit Concept. More about Limits. The Concept of Continuity.

3. The Derivative.

The Derivative and Rates of Change. Basic Differentiation Rules. The Chain Rule. Derivatives of Algebraic Functions. Maxima and Minima of Functions on Closed Intervals. Applied Optimization Problems. Derivatives of Trigonometric Functions. Successive Approximations and Newton's Method.

4. Additional Applications of the Derivative.

Implicit Functions and Related Rates. Increments, Differentials, and Linear Approximation. Increasing and Decreasing Functions and the Mean Value Theorem. The First Derivative Test and Applications. Simple Curve Sketching. Higher Derivatives and Concavity. Curve Sketching and Asymptotes.

5. Calculus of Transcendental Functions.  Inverse Trigonometric Functions.

10. Analytic Geometry and the Conic Sections.  Conic Sections and Applications.

Course Objectives/ Course outcome:

To provide students with knowledge and understanding of a range of  mathematical techniques appropriate to engineering.

At the end of this set of modules the student should be able to:
manipulate algebraic expressions and equations.
Understand and apply appropriately inverse functions, trigonometric functions, polynomial functions, rational functions, circular functions, conic section.

Understand the concept of Limit and continuity.

Understand the meaning of a derivative, be able to differentiate simple functions, products and quotients, and be able to use the chain rule and differentials.

In particular the course will concentrate on learning to use mathematics as a tool and will include many worked examples.

Class/ Tutorial (Laboratory) Schedule

Three  one -hour lecture sessions and two one - hour tutorial sessions per week.

Assessment Tools

1. Final Examination
2. Mid term examinations
3. Homework Assignments
4. Class Quizzes
5. Attendance
6. Tutorial Judgment

Prepared by

Dr. Khawaja Zafar Elahi   [ kzelahi@ksu.edu.sa]