[vc_row el_class=”inner-body-content” css=”.vc_custom_1666845084769{padding-top: 30px !important;padding-bottom: 20px !important;}”][vc_column][vc_custom_heading text=”COURSE OBJECTIVES” use_theme_fonts=”yes” css=”.vc_custom_1666845070188{margin-top: 0px !important;}”][vc_column_text]

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

[/vc_column_text][vc_custom_heading text=”COURSE LEARNING OUTCOMES (CLO)” use_theme_fonts=”yes”][vc_column_text]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.[/vc_column_text][vc_custom_heading text=”COURSE CONTENTS” use_theme_fonts=”yes”][vc_column_text css=”.vc_custom_1666845026684{margin-bottom: 0px !important;}”]

**Limits and Continuity**- Introduction to limits
- Rates of change
- Continuity

**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

**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

**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

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