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 To define and explain the ideas of differential and integral calculus. (C2)
CLO:2 To apply derivatives and integrals for solving different problems arising in engineering sciences. (C3)
CLO:3 To use vector calculus and analytical geometry in multiple dimensions. (C3)
CLO:4 To clarify his/her solutions of engineering problems by the application of calculus and analytical geometry.(A2)

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
    • Radius of gyration
    • Fubini’s theorem for calculating double integrals
    • Areas moments and centers of mass
    • Centroid of a plane figure
    • Centre of gravity of a solid of revolution
    • Moment of inertia
    • Second moment of area
    • Centers of pressure and depth of centre of pressure.
    • Triple integrals, volume of a region in space
    • Volumes of solids of revolution
    • Curvature, radius and centre of curvature