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.
- Limits and Continuity
- Introduction to limits
- Rates of change
- 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
- 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
- Transcendental functions
- Inverse functions
- Hyperbolic and trigonometric identities and their relationship
- Logarithmic and exponential functions
- 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
- 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