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# Differential equations

CEC and Farook College via Swayam

### Overview

The course is developed to enable the undergraduate students to get a comprehensive understanding and applications of the differential equations. This course includes the study of first order differential equations, higher order linear differential equations, boundary value and initial value problems, and applications of differential equations. The primary Learning Outcome for this course is Quantitative Reasoning, which is to understand and apply mathematical concepts and reasoning, and analyze and interpret various types of data. The Learning Outcome will be assessed through targeted questions on either the comprehensive final or an outside assignment. In an increasingly complex world, mathematical thinking, understanding, and skill are more important than ever. Differential equations will provide students with the needed working knowledge of advanced mathematical concepts and an awareness of their relationship to complex problems. Students wishing to major in the sciences or engineering are required to study differential equations. It provides a solid foundation for further study in mathematics, the sciences, and engineering. Differential Equations provides students with skills for proficiency in first order differential equations, higher order linear differential equations and a conceptual understanding of those topics, and the opportunity for an in-depth understanding of elementary differential equations and the meaning of their solutions.

### Syllabus

Week 1 Day 1 : Introduction to Differential Equations. Day 2 : Solutions of Differential Equations. Day 3 : Solving Differential Equations by Variable Separable Method   Week 2 Day 1 : Equations Reducible to Reparable form – Substitution Method -Part 1 Day 2 : Equations Reducible To Separable Form – Substitution Method – Part 2 Day 3 : Reducible To Separable Form - Homogeneous Equation.   Week 3 Day 1 : Equations Reducible To Separable Form Via Reducing To Homogeneous Form Day 2 : Exact Differential Equation- Part I Day 3 : Exact Differential Equation- Part II   Week 4 Day 1 : Differential Equation : Integrating Factors Day 2 : Linear First Order Differential Equations – Part 1 Day 3 : Linear First Order Differential Equations – Part 2   Week 5 Day 1 : Linear First Order Differential Equations – Part 3 Day 2 : Solving Linear Differential Equations By Method Of Variation Of Paremeters. Day 3 : Bernoulli’s Differential Equation – Part 1   Week 6 Day 1 : Bernoulli’s Differential Equation – Part 2 Day 2 : Second Order Differential Equations. Day 3 : Fundamental theorem.   Week 7 Day 1 : General Solution and Basis Day 2 : Initial value Problem and Boundary Value Problem. Day 3 : Second Order Differential Equations with Constant Coefficients – Part I.   Week 8 Day 1 : Second Order Differential Equations with Constant Coefficients – Part II. Day 2 : Second Order Differential Equations with Constant Coefficients – Part III. Day 3 : Differential Operator   Week 9 Day 1 : Euler - Cauchy Equation – Part I Day 2 : Euler - Cauchy Equation – Part II Day 3 : Euler - Cauchy Equation – Part III   Week 10 Day 1 : Existence and Uniqueness Theory: Wronskian. Day 2 : Non Homogeneous Equations – Part I Day 3 : Method of Undetermined Coefficients– Part I   Week 11 Day 1 : Method of Undetermined Coefficients– Part II Day 2 : Method of Undetermined Coefficients– Part III Day 3 : Method of Undetermined Coefficients– Part IV   Week 12 Day 1 : Method of Undetermined Coefficients– Part V Day 2 : Method of Undetermined Coefficients– Part VI Day 3 : Method of Variation of Parameters– Part I   Week 13 Day 1 : Method of Variation of Parameters– Part II Day 2 : Method of Variation of Parameters: Euler – Cauchy Equation. Day 3 : Applications of Differential Equations – Part I.   Week 14 Day 1 : Applications of Differential Equations – Part I Day 2 : Interaction based on the entire Modules covered. Day 3 : Revision Day 4 : Revision Day 5 : Term end assessment

### Taught by 