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Swayam
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Description
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.
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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
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TypeOnline Courses
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ProviderSwayam
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.
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
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