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 Pre / Co-requisite
Basic knowledge in single variable calculus.
Course Outcomes
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
Mapping of Course Outcomes with Program Outcomes and Program Specific Outcomes
PO/ | PO1 | PO2 | PO3 | PO4 | PO5 | PO6 | PO7 | PO8 | PO9 | PO10 | PO11 | PO12 |
PSO1 |
PSO2 |
PSO3 |
CO1 | H | H | M | M | M | M | M | H | |||||||
CO2 | H | H | M | M | M | H | |||||||||
CO3 | H | H | M | M | M | H | |||||||||
CO4 | H | H | M | M | M | H |
Curriculum
- 4 Sections
- 36 Lessons
- 10 Weeks
- Module 1-Partial DerivativesLimit of functions of more than one variable9
- 1.1Limits60 Minutes
- 1.2Continuity35 Minutes
- 1.3Partial Derivatives of Functions of Two Variables30 Minutes
- 1.4Partial Derivatives of Higher Order30 Minutes
- 1.5Mixed Partial Derivatives30 Minutes
- 1.6Local Linear Approximation40 Minutes
- 1.7Chain rule40 Minutes
- 1.8Implicit differentiation30 Minutes
- 1.9Maxima and minima of functions of two variables40 Minutes
- Module 2 Multiple Integrals9
- 2.1Double Integrals50 Minutes
- 2.2Reversing the order of integration in double integrals30 Minutes
- 2.3Change of coordinates in double integrals30 Minutes
- 2.4Evaluating areas using double integrals35 Minutes
- 2.5Finding volumes using double integrals35 Minutes
- 2.6Triple integrals30 Minutes
- 2.7Volume calculated as triple integrals35 Minutes
- 2.8Triple integrals in cartesian and cylindrical co ordinates30 Minutes
- 2.9More problems in triple integrals30 Minutes
- Calculus of vector functions9
- 3.1Vector valued function of a single variable-Derivative of vector valued function
- 3.2Concept of scalar and vector fields
- 3.3Directional Derivatives
- 3.4Divergent and Curl
- 3.5Line Integrals of vector fields
- 3.6Work done as a Line integral
- 3.7Conservative Vector Field40 Minutes
- 3.8Independence of path,Potential function40 Minutes
- 3.9More problems25 Minutes
- Vector Integral Theorems9
- 4.1Green’s Theorem and applications to evaluating line integrals80 Minutes
- 4.2Finding Areas using Green’s Theorem20 Minutes
- 4.3Surface Integrals50 Minutes
- 4.4Divergence Theorem
- 4.5Using Divergence Theorem to find flux
- 4.6Stoke’s Theorem25 Minutes
- 4.7More problems on Stoke’s Theorem40 Minutes
- 4.8More problems on Divergence Theorem20 Minutes
- 4.9More problems on Green’s Theorem