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


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)


  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