Multiple Integration and Its Applications - Calculus (Undergraduate Advanced)
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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.
MTH 201: Mathematical Methods IMastering advanced calculus is essential for modelling complex systems in science and engineering. This track delivers the rigorous mathematical foundation demanded by the official NUC CCMAS curriculum for MTH 201. It systematically builds your expertise from fundamental single-variable theory to the sophisticated multivariable analysis used to solve critical problems in physics, economics, and technology.
This programme is for undergraduates in engineering, mathematics, physics, and computer science requiring a deep theoretical and practical command of calculus. It also serves economics students needing advanced quantitative tools or professionals in finance and data science seeking a solid mathematical base for technical research.
You will gain the analytical skills to construct formal proofs for differentiation rules and apply cornerstone theorems like Mean Value and Taylor's. You will master multivariable techniques, enabling you to solve constrained optimization problems with Lagrange multipliers and compute multiple integrals across line, surface, and volume domains. This track is the requisite preparation for advanced studies in differential equations, vector analysis, and complex engineering modelling.
Mastering advanced calculus is essential for modelling complex systems in science and engineering. This track delivers the rigorous mathematical foundation demanded by the official NUC CCMAS curriculum for MTH 201. It systematically builds your expertise from fundamental single-variable theory to the sophisticated multivariable analysis used to solve critical problems in physics, economics, and technology. This programme is for undergraduates in engineering, mathematics, physics, and computer science requiring a deep theoretical and practical command of calculus. It also serves economics students needing advanced quantitative tools or professionals in finance and data science seeking a solid mathematical base for technical research. You will gain the analytical skills to construct formal proofs for differentiation rules and apply cornerstone theorems like Mean Value and Taylor's. You will master multivariable techniques, enabling you to solve constrained optimization problems with Lagrange multipliers and compute multiple integrals across line, surface, and volume domains. This track is the requisite preparation for advanced studies in differential equations, vector analysis, and complex engineering modelling.
Course Chapters
1. Introduction7
A review of the methods of integration of single-variable functions.
Chapter lessons
1-5. Techniques of integration (1)14:51
1-6. Techniques of integration (2)27:39
2. Line Integrals63
Meaning and methods of evaluation of line integrals.
Chapter lessons
2-6. Conservative vector fields14:55
3. Double Integrals23
Meaning, methods of evaluation and applications of double integrals.
Chapter lessons
3-1. Definition20:39
Meaning and symbols for double integrals.
3-2. Change of variables24:46
How to evaluate double integrals by change of variables.
4. Applications of Double Integrals51
Applications of double integrals to areas, volumes, total masses, centres of gravity, moments of inertia, etc.
Chapter lessons
4-1. Area and centroid14:37
Calculation of area and centroid of a region R in a plane by double integration.
4-2. Area moments of inertia5:01
Calculating area moments of inertia of a region R in a plane by double integration.
4-3. Volume3:12
Calculation of volume beneath a surface and above a region R in a plane by double integration.
4-4. Mass and centre of gravity18:24
Calculation of total mass and centre of gravity by double integration.
4-5. Mass moments of inertia6:29
Meaning and calculation of mass moments of inertia by double integration.
5. Green's Theorem23
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. Theorem15:28
Statement of Green's theorem in a plane and its use in evaluating line integrals by double integrals, and vice-versa.
5-2. Proof34:30
Proof of Green's theorem in a plane.
6. Surface Integrals43
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 Theorem12
Statement, meaning, proof and applications of Stoke's theorem.
Chapter lessons
7-1. Theorem
Statement of Stoke's theorem and its application.
8. Triple Integrals22
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' Theorem11
Statement, meaning, proof and applications of Gauss' theorem.
Chapter lessons
9-1. Theorem
Statement of Gauss' theorem and its application.