Multiple Integration and Its Applications
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CHE 305: Engineering Analysis IAdvanced 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
1Introduction
A review of the methods of integration of single-variable functions.
Chapter lessons
5.Techniques of integration (1)14:51
6.Techniques of integration (2)27:39
2Line Integrals
Meaning and methods of evaluation of line integrals.
Chapter lessons
6.Conservative vector fields14:55
8.Worked examples (2)8:54
3Double Integrals
Meaning, methods of evaluation and applications of double integrals.
Chapter lessons
1.Definition20:39
Meaning and symbols for double integrals.
2.Change of variables24:46
How to evaluate double integrals by change of variables.
3.Worked examples (1)7:31
Worked examples on evaluation of double integrals.
4.Worked examples (2)17:24
More worked examples on evaluation of double integrals - involving change of variables.
5.Worked examples (3)19:48
More worked examples on evaluation of double integrals - involving change of variables.
4Applications of Double Integrals
Applications of double integrals to areas, volumes, total masses, centres of gravity, moments of inertia, etc.
Chapter lessons
1.Area and centroid14:37
Calculation of area and centroid of a region R in a plane by double integration.
2.Area moments of inertia5:01
Calculating area moments of inertia of a region R in a plane by double integration.
3.Volume3:12
Calculation of volume beneath a surface and above a region R in a plane by double integration.
4.Mass and centre of gravity18:24
Calculation of total mass and centre of gravity by double integration.
5.Mass moments of inertia6:29
Meaning and calculation of mass moments of inertia by double integration.
6.Worked examples (1)51:02
Worked examples on applications of double integrals to areas, volumes, total masses, centres of gravity, moments of inertia, etc.
5Green's Theorem
Statement, meaning, proof and applications of Green's theorem in a plane - the two-dimensional form of the fundamental theorem of calculus.
Chapter lessons
1.Theorem15:28
Statement of Green's theorem in a plane and its use in evaluating line integrals by double integrals, and vice-versa.
2.Proof34:30
Proof of Green's theorem in a plane.
3.Worked examples (1)9:11
Worked examples on evaluating line or double integrals using Green's theorem.
4.Worked examples (2)51:38
More worked examples on evaluating line or double integrals using Green's theorem.
5.Worked examples (3)6:55
More worked examples on evaluating line or double integrals using Green's theorem.
6Surface Integrals
Meaning and methods of evaluation of surface integrals.
Chapter lessons
1.Definition
Meaning and symbols for surface integrals, in contrast to line integrals.
2.Differential surface
How to obtain the differential (elemental) surface area for surface integrals.
3.Parametric surfaces
Parametric representation of common surfaces.
4.Forms of surface integrals
Scalar and vector forms of surface integrals and how to evaluate them.
5.Worked examples (1)
Worked examples on evaluation and applications of surface integrals.
6.Worked examples (2)
More worked examples on evaluation and applications of surface integrals.
7.Worked examples (3)
More worked examples on evaluation and applications of surface integrals.
7Stoke's Theorem
Statement, meaning, proof and applications of Stoke's theorem.
Chapter lessons
1.Theorem
Statement of Stoke's theorem and its application.
2.Worked examples (1)
Worked examples on applications of Stoke's theorem.
3.Worked examples (2)
Worked examples on applications of Stoke's theorem.
8Triple Integrals
Meaning and methods of evaluation of triple integrals.
Chapter lessons
1.Definition
Meaning and symbols for triple integrals, in contrast to double integrals.
2.Evaluation
How to evaluate triple integrals.
3.Worked examples (1)
Worked examples on evaluation and applications of triple integrals.
4.Worked examples (2)
More worked examples on evaluation and applications of triple integrals.
9Gauss' Theorem
Statement, meaning, proof and applications of Gauss' theorem.
Chapter lessons
1.Theorem
Statement of Gauss' theorem and its application.
2.Worked examples (1)
Worked examples on applications of Gauss' theorem.