Multiple Integration and Its Applications - Calculus (Undergraduate Advanced)

Multiple Integration and Its Applications - Calculus (Undergraduate Advanced)

Multiple integration; line, surface and volume integrals.

9

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Enrolment valid for 12 months

This course is also part of the following learning track. You may join the track to gain comprehensive knowledge across related courses.

[OAU, Ife] CHE 305: Engineering Analysis I

Advanced engineering mathematics covering solid analytical geometry, integrals, scalar and vector fields, matrices and determinants and complex variables. Curated for third-year students of engineering at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.

Advanced engineering mathematics covering solid analytical geometry, integrals, scalar and vector fields, matrices and determinants and complex variables. Curated for third-year students of engineering at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.

Course Chapters

1. Introduction

7

A review of the methods of integration of single-variable functions.

Chapter lessons

1-1. Welcome

9:30

Welcome to the course and overview of course content.

1-2. Definition

20:21

Meaning of integration and its associated symbols.

1-3. Properties of integrals

21:30

Properties of integrals of real-valued single-variable functions.

1-4. Standard integrals

19:21

Overview of common functions and their integrals.

1-5. Techniques of integration (1)

14:51

A review of the techniques of integration of single-variable real-valued functions.

1-6. Techniques of integration (2)

27:39

A review of the techniques of integration of single-variable real-valued functions.

1-7. Techniques of integration (3)

21:10

A review of the techniques of integration of single-variable real-valued functions.

2. Line Integrals

6

3

Meaning and methods of evaluation of line integrals.

Chapter lessons

2-1. Definition

25:19

Meaning of line integral, in contrast to a definite integral along the x-axis.

2-2. Differentials

14:55

Scalar and vector differentials used in line integrals.

2-3. Parametric curves

39:28

Parametric forms of equations of straight and curved lines.

2-4. Forms of line integrals

14:55

Different forms of line integrals and how to evaluate them.

2-5. Properties

4:33

General properties of line integrals.

2-6. Conservative vector fields

14:55

Meaning and properties of line integrals of conservative vector fields - path independence of their line integrals.

3. Double Integrals

2

3

Meaning, methods of evaluation and applications of double integrals.

Chapter lessons

3-1. Definition

20:39

Meaning and symbols for double integrals.

3-2. Change of variables

24:46

How to evaluate double integrals by change of variables.

4. Applications of Double Integrals

5

1

Applications of double integrals to areas, volumes, total masses, centres of gravity, moments of inertia, etc.

Chapter lessons

4-1. Area and centroid

14:37

Calculation of area and centroid of a region R in a plane by double integration.

4-2. Area moments of inertia

5:01

Calculating area moments of inertia of a region R in a plane by double integration.

4-3. Volume

3:12

Calculation of volume beneath a surface and above a region R in a plane by double integration.

4-4. Mass and centre of gravity

18:24

Calculation of total mass and centre of gravity by double integration.

4-5. Mass moments of inertia

6:29

Meaning and calculation of mass moments of inertia by double integration.

5. Green's Theorem

2

3

Statement, meaning, proof and applications of Green's theorem in a plane - the two-dimensional form of the fundamental theorem of calculus.

Chapter lessons

5-1. Theorem

15:28

Statement of Green's theorem in a plane and its use in evaluating line integrals by double integrals, and vice-versa.

5-2. Proof

34:30

Proof of Green's theorem in a plane.

6. Surface Integrals

4

3

Meaning and methods of evaluation of surface integrals.

Chapter lessons

6-1. Definition

Meaning and symbols for surface integrals, in contrast to line integrals.

6-2. Differential surface

How to obtain the differential (elemental) surface area for surface integrals.

6-3. Parametric surfaces

Parametric representation of common surfaces.

6-4. Forms of surface integrals

Scalar and vector forms of surface integrals and how to evaluate them.

7. Stoke's Theorem

1

2

Statement, meaning, proof and applications of Stoke's theorem.

Chapter lessons

7-1. Theorem

Statement of Stoke's theorem and its application.

8. Triple Integrals

2

2

Meaning and methods of evaluation of triple integrals.

Chapter lessons

8-1. Definition

Meaning and symbols for triple integrals, in contrast to double integrals.

8-2. Evaluation

How to evaluate triple integrals.

9. Gauss' Theorem

1

1

Statement, meaning, proof and applications of Gauss' theorem.

Chapter lessons

9-1. Theorem

Statement of Gauss' theorem and its application.