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Calculus

Course Description: Infinite sequences, convergence and divergence of infinite series, integral test, ratio test, root test, and comparison test. Conditional and absolute convergence, alternating series test. Power series. Taylor and Maclaurin series. Functions of two or three variables, their limits, continuity, and differentiability, chain rule, directional derivatives; gradient, tangent planes, maxima and minima of functions of two or three variables, Lagrange multipliers, double integrals and their applications to area, volume, moments, and center of mass. Double integrals in polar coordinates. Triple integrals in rectangular, cylindrical, and spherical coordinates and their applications to volume, moment, and center of mass. Vector fields, line integrals, surface integrals, Green's theorem, divergence theorem. Stoke's theorem.

Credit hours: 3

Prerequisites: MATH106

Objectives of the course :

The main objectives of the course:

Application of concepts of limits, continuity, and partial derivatives for functions of two or more variables.

2. Description of increasing and decreasing sequences and their convergence.

3. Finding pointwise convergent sequences of functions.

4. Determine directional derivatives, tangent planes, and extrema of functions of two or three variables.

5. Calculation of multiple integrals and their applications.

6. Explanation of the meaning of curl, divergence of vectors, and gradient of scalar quantities, and their properties with applications such as line integrals, surface integrals, Green's theorem, the divergence theorem, and others.

Course outputs :

Knowledge and understanding:

1.1 Description of Sequence Convergence. (K1)

1.2 Recognize tests for convergence of series; and determine the sum of infinite series. (K1)

1.3 Explanation of the basic concepts of functions of two or more variables. (K1)

1.4 Study of Maxima and Minima, and Directional Derivatives of Functions of Several Variables. (K1)

1.5 Explanation of the basic concepts of vector fields, gradient, divergence, curl, and their properties. (K1)

1.6 Description of line and surface integrals. (K1)

Skills:
2.1 Discussion of the limits and continuity of functions of two or more variables. (S1)

2.2 Discussion of Partial Derivatives, the Chain Rule, and Tangent Planes. (S1)

2.3 Solving Multiple Integrals and Discussing Their Applications. (S1)

2.4 Solving Problems Using Green's, Divergence, and Stokes' Theorems. (S1)

Additional information:

Course Content:

1. Sequences, monotonic sequences

2. Infinite sequences, divergence test, integral test, p-series.

3. Comparison Tests, Ratio Test, and Root Test; Alternating Series Test.

4. Conditional and absolute convergence; power series, Maclaurin, and Taylor.

5. Functions in two or three variables, their limits, continuity, differentiability, partial derivatives, chain rule.

6. Directional Derivatives; Gradient, Tangent Planes.

7. Maximum and minimum values of functions in two or three variables.

8. Lagrange Multipliers, Double Integrals.

9. Applications of Double Integrals; Triple Integrals.

10. Applications of Triple Integrals; Vector Fields, Divergence, and Curl.

11. Line Integrals; Green's Theorem.

12. Surface Integrals; Divergence Theorem, Stokes' Theorem.

Last updated: 2026-05-05