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Main
UQU Programs
Mathematics

Multi-variables Calculus

MTH2103
4 hours English

Multi-variables Calculus

Multi variables Calculus
MTH1102 Calculus 2
4 hours One requisite
1 Vectors: / Cartesian coordinates in three-Space, / Vectors, / The dot product, / The cross product, / Vector-valued functions, / Lines and tangent lines in space / Cylindrical and spherical coordinates
2 Functions of several variables: / Functions of two or more variables, / Partial derivatives, / Limits and continuity / Differentiability, / Directional derivatives and gradients, / The chain rule, / Maxima and Minima
3 Multiple integrals and their applications: / Double integrals over rectangles, / Iterated integrals, / Double integrals over Nonrectangular regions, / Double integrals in polar coordinates, / Applications of double integrals, / Surface area, / Triple integrals in cartesian coordinates, / Triple integrals in cylindrical and spherical coordinates, / Change of variables in Multiple integrals
4 Vector calculus: / Vector fields, / Line integrals, / Independence of path, / Green’s theorem in the plane
5 Revision
1.1 Mapped to: K1, K2

Develop knowledge and understanding on unit tangents, normal vectors, and curvature of curves determined by vector-valued functions.

Teaching Strategy Lectures, exercises
Assessment Methods Homework, Midterm and final Exams.
1.2 Mapped to: K1, K2

Show familiarity with various concepts related to functions of several variables and multiple integrals using cartesian, polar, cylindrical and spherical coordinates.

Teaching Strategy Lectures, problem-based learning
Assessment Methods Homework, Midterm and final Exams.
2.1 Mapped to: S4, S6

Determine domains and ranges of functions of several variables and sketch their graphs and level curves.

Teaching Strategy Lectures, exercises
Assessment Methods Homework, Midterm and final Exams.
2.2 Mapped to: S1, S5, S7

Investigate the limits and continuity of a function of several variables.

Teaching Strategy Lectures, exercises
Assessment Methods Homework, Midterm and final Exams.
2.3 Mapped to: S1

Find partial derivatives and use them to obtain directional derivatives, gradients, equations of tangent planes, normal lines, critical points, and extrema.

Teaching Strategy Lectures, exercises
Assessment Methods Homework, Midterm and final Exams.
2.4 Mapped to: S1, S6

Evaluate multiple integrals in rectangular, polar, cylindrical, and spherical coordinate systems and use the Jacobian to make a change of variables.

Teaching Strategy Lectures, exercises
Assessment Methods Homework, Midterm and final Exams.
2.5 Mapped to: S2

Apply multiple integrals to compute areas, surface areas, and volumes.

Teaching Strategy Lectures, project report
Assessment Methods Homework, Midterm and final Exams.
2.6 Mapped to: S1, S7

Evaluate the line integrals of functions of several variables along curves, characterize the independence of path , and apply Green’s theorem.

Teaching Strategy Lectures, exercises
Assessment Methods Homework, Midterm and final Exams.
3.1 Mapped to: V1, V2

Develop self-learning skills and solve problems both individually and in collaboration with the classmates

Teaching Strategy Lectures, project report
Assessment Methods Homework and assignments.
Assessment
Weight
Midterm exam
30%
Homework and assignments
20%
Final Exam
50%
Total
100%