Course Code: GYMAT201
Course Name: MATHEMATICS FOR ELECTRICAL SCIENCE AND PHYSICAL SCIENCE – 2
Prerequisites: Basic knowledge in single variable calculus
Course Objectives: To provide a comprehensive understanding of partial derivatives, multiple integrals, and the differentiation and integration of vector-valued functions, emphasizing their applications in engineering contexts.
Course Outcomes (COs):
At the end of the course students should be able to:
CO1: Compute the partial and total derivatives and maxima and minima of multivariable functions and to apply in engineering problems.
CO2: Understand theoretical idea of multiple integrals and to apply them to find areas and volumes of geometrical shapes.
CO3: Compute the derivatives and line integrals of vector functions and to learn their applications.
CO4: Apply the concepts of surface and volume integrals and to learn their inter-relations and applications.
Curriculum
- 4 Sections
- 36 Lessons
- 5 Weeks
- MODULE 1- PARTIAL DERIVATIVES9
- 1.1LESSON 1 – LIMIT OF FUNCTIONS25 Minutes
- 1.2LESSON 2 – CONTINUITY OF FUNCTIONS40 Minutes
- 1.3LESSON 3- PARTIAL DERIVATIVES60 Minutes
- 1.4LESSON 4 – SLOPE AND RATE OF CHANGE30 Minutes
- 1.5LESSON 5 – HIGHER ORDER PARTIAL DERIVATIVES60 Minutes
- 1.6LESSON 6 – LOCAL LINEAR APPROXIMATION40 Minutes
- 1.7LESSON 7 – CHAIN RULE30 Minutes
- 1.8LESSON 8 – IMPLICIT DIFFERENTIATION30 Minutes
- 1.9LESSON 9 – MAXIMA AND MINIMA40 Minutes
- MODULE 2-MULTIPLE INTEGRALS9
- 2.1LESSON 1-DOUBLE INTEGRALS40 Minutes
- 2.2LESSON 2 -REVERSING THE ORDER OF INTEGRATION IN DOUBLE INTEGRALS30 Minutes
- 2.3LESSON 3 – CHANGE OF COORDINATES IN DOUBLE INTEGRAL-(CARTESIAN TO POLAR)30 Minutes
- 2.4LESSON 4 – EVALUATING AREA USING DOUBLE INTEGRALS30 Minutes
- 2.5LESSON 5 – FINDING VOLUME BY DOUBLE INTEGRALS30 Minutes
- 2.6LESSON 6 – TRIPLE INTEGRALS30 Minutes
- 2.7LESSON 7 – VOLUME CALCULATED AS TRIPLE INTEGRALS30 Minutes
- 2.8LESSON 8 – TRIPLE INTEGRALS IN CARTESIAN AND CYLINDRICAL COORDINATES30 Minutes
- 2.9LESSON 9 -TRIPLE INTEGRALS -MORE PROBLEMS50 Minutes
- MODULE 3 - VECTOR CALCULUS9
- 3.1LESSON 1 – CALCULUS OF VECTOR FUNCTIONS25 Minutes
- 3.2LESSON 2- DERIVATIVES OF VECTOR FUNCTIONS25 Minutes
- 3.3LESSON 3 – GRADIENT50 Minutes
- 3.4LESSON 4 – DIRECTIONAL DERIVATIVE50 Minutes
- 3.5LESSON 5 – DIVERGENCE AND CURL50 Minutes
- 3.6LESSON 6 – LINE INTEGRALS – TYPE 130 Minutes
- 3.7LESSON 7 – LINE INTEGRALS TYPE II30 Minutes
- 3.8LESSON 8 – WORK DONE AS LINE INTEGRAL40 Minutes
- 3.9LESSON 9 – CONSERVATIVE VECTOR FIELD AND POTENTIAL FUCTION40 Minutes
- MODULE 4 -VECTOR INTEGRAL THEOREMS9
- 4.1LESSON 1 – GREEN’S THEOREM40 Minutes
- 4.2LESSON 2 – WORK DONE BY GREEN’S THEOREM30 Minutes
- 4.3LESSON 3 – AREA BY GREEN’S THEOREM25 Minutes
- 4.4LESSON 4 – SURFACE INTEGRALS30 Minutes
- 4.5LESSON 5 – SURFACE INTEGRALS- MORE PROBLEMS20 Minutes
- 4.6LESSON 6 – DIVERGENCE THEOREM25 Minutes
- 4.7LESSON 7 – DIVERGENCE THEOREM – MORE PROBLEMS20 Minutes
- 4.8LESSON 8 – STOKE’S THEOREM25 Minutes
- 4.9LESSON 9 – STOKE’S THEOREM – MORE PROBLEMS20 Minutes