COURSE OBJECTIVES

This course provides an introduction to the theory, solution, and application of ordinary differential equations. Topics discussed in the course include methods of solving first-order differential equations, existence and uniqueness theorems, second-order linear equations, power series solutions, higher-order linear equations, and their applications.

COURSE LEARNING OUTCOMES (CLO)


CLO: 1. Use their knowledge of calculus to solve the 1st order ordinary differential equations
CLO: 2. Use various techniques to solve higher order ordinary differential.
CLO: 3. Model the problems arising in different areas of science and engineering in the form of ordinary differential equations.
CLO: 4. Understand the meaning, use and applications of the partial differential equations

COURSE CONTENTS

  1. Limits and Continuity– Four Lectures
    • Introduction to Limits
    • Rates of Change and Limits
    • One-Sided Limits, Infinite Limits
    • Continuity, Continuity at a Point, Continuity on an interval
  2. Differentiation– Six Lectures
    • Definition and Examples
    • Relation Between Differentiability and Continuity
    • Derivative as slope, as rate of change (graphical representation).
    • The Chain Rule
    • Applications of Ordinary Derivatives
  3. Integration– Five Lectures
    • Indefinite Integrals
    • Different Techniques for Integration
    • Definite Integrals
    • Riemann Sum, Fundamental Theorem of Calculus
    • Area Under the Graph of a Nonnegative Function
    • Improper Integrals
  4. Transcendental Functions– Five Lectures
    • Inverse functions
    • Logarithmic and Exponential Functions
    • Inverse Trigonometric Function
    • Hyperbolic Functions and Inverse Hyperbolic Functions
    • More Techniques of Integration
  5. Analytical Geometry– Six Lectures
    • Three Dimensional Geometry
    • Vectors in Spaces
    • Vector Calculus
    • Directional Derivatives
    • Divergence, Curl of a Vector Field
    • Multivariable Functions
    • Partial Derivatives
  6. Analytical Geometry– Six Lectures
    • Conic Sections
    • Parameterizations of Plane Curves
    • Vectors in Plane, Vectors in space
    • Dot Products, Cross Products
    • Lines and Planes in Space
    • Spherical, Polar and Cylindrical Coordinates.
    • Vector-Valued Functions and Space Curves
    • Arc-Length and Tangent Vector
    • Curvature, Torsion and TNB Frame
    • Fubini’s Theorem for Calculating Double Integrals
    • Areas Moments and Centers of Mass
    • Triple Integrals, Volume of a Region in Space