## COURSE OBJECTIVES

1. To learn fundamentals of mathematics, calculus and analytical geometry.
2. To enable students to apply the ideas to solve problems of practical nature.

## COURSE LEARNING OUTCOMES (CLO)

CLO:1 Have knowledge related to the fundamentals of calculus and analytical geometry.
CLO:2 Understand the differentiation integration and their applications.
CLO:3 Apply the acquired knowledge to solve problems of practical nature.

## COURSE CONTENTS

1. Limits and Continuity
• Introduction to limits
• Rates of change
• Continuity
2. Differentiation
• Definition and examples
• Relation between differentiability and continuity
• Equations of tangents and normals
• Derivative as slope, as rate of change (graphical representation)
• Differentiation and successive differentiation and its application to rate, speed and acceleration
• Maxima and minima of function of one variable and its applications
• Convexity and concavity
• Points of inflexion
3. Integration
• Indefinite integrals
• Definite integrals
• Integration by substitution, by partial fractions and by parts
• Integration of trigonometric functions
• Riemann sum, fundamental theorem of calculus
• Area under the graph of a nonnegative function
• Area between curves
• Improper integrals
4. Transcendental functions
• Inverse functions
• Hyperbolic and trigonometric identities and their relationship
• Logarithmic and exponential functions
5. Vector calculus
• Three-dimensional geometry
• Vectors in spaces
• Rectangular and polar co-ordinate systems in three dimensions
• Direction cosines
• Plane (straight line) and sphere.
• Partial derivatives
• Partial differentiation with chain rule
• Total derivative
• Divergence, curl of a vector field
6. Analytical geometry
• Arc-length and tangent vector
• Lengths of curves