Faculty Of Engıneerıng
Industrıal Engıneerıng (Englısh)
Course Information
MATHEMATICS II | |||||
---|---|---|---|---|---|
Code | Semester | Theoretical | Practice | National Credit | ECTS Credit |
Hour / Week | |||||
MAT104 | Spring | 4 | 0 | 4 | 6 |
Prerequisites and co-requisites | |
---|---|
Language of instruction | English |
Type | Required |
Level of Course | Bachelor's |
Lecturer | Asst. Prof. Dr. Türker Ertem |
Mode of Delivery | Face to Face |
Suggested Subject | None |
Professional practise ( internship ) | None |
Objectives of the Course | The sequence MAT 103-104 is the standard complete introduction to the concepts and methods of calculus. It is taken by all engineering students. The emphasis is on concepts, solving problems, theory and proofs. All sections are given a uniform midterm and a final exam. Students will develop their reading, writing and questioning skills in mathematics. |
Contents of the Course | Sequences and infinite series. Power series. Taylor series. Vectors and analytic geometry in 3-space. Functions of several variables: limits, continuity, partial derivatives. Chain rule. Directional derivatives. Tangent planes and linear approximations. Extreme values. Lagrange multipliers. Double integrals. Double integrals in polar coordinates. General change of variables in double integrals. Surface parametrization and surface area in double integrals. Triple integrals in Cartesian, cylindrical and spherical coordinates. Parametrization of space curves. Line integrals. Path independence. Green s theorem in the plane. |
Learning Outcomes of Course
# | Learning Outcomes |
---|---|
1 | To effectively write mathematical solutions in a clear and concise manner. |
2 | To graphically and analytically synthesize and to apply multivariable and vector-valued functions and their derivatives, using correct notation and mathematical precision. |
3 | To use double, triple and line integrals in applications, including Green's Theorem. |
4 | To synthesize the key concepts of differential, integral and multivariate calculus. |
Course Syllabus
# | Subjects | Teaching Methods and Technics |
---|---|---|
1 | Ch. 9: Sequences, Series, and Power Series 9.1 Sequences and Convergence 9.2 Infinite Series 9.3 Convergence Tests for Positive Series | lecturing, discussing, problem solving |
2 | 9.3 Convergence Tests for Positive Series 9.4 Absolute and Conditional Convergence | lecturing, discussing, problem solving |
3 | 9.5 Power Series 9.6 Taylor and Maclaurin Series | lecturing, discussing, problem solving |
4 | 9.7 Applications of Taylor and Maclaurin Series Ch. 10: Vectors and Coordinate Geometry in 3-Space 10.1 Analytic Geometry in Three Dimensions 10.2 Vectors | lecturing, discussing, problem solving |
5 | 10.3 The Cross Product in 3-Space 10.4 Planes and Lines 10.5 Quadric Surfaces Ch. 12: Partial Differentiation 12.1 Functions of Several Variables | lecturing, discussing, problem solving |
6 | 12.2 Limits and Continuity 12.3 Partial Derivatives 12.4 Higher-Order Derivatives 12.5 The Chain Rule | lecturing, discussing, problem solving |
7 | 12.6 Linear Approximations, Differentiability, and Differentials 12.7 Gradients and Directional Derivatives | lecturing, discussing, problem solving |
8 | 12.8 Implicit Functions Ch. 13: Applications of Partial Derivatives 13.1 Extreme Values 13.2 Extreme Values of Functions Defined on Restricted Domains | lecturing, discussing, problem solving |
9 | 13.3 Lagrange Multipliers Ch. 14: Multiple Integration 14.1 Double Integrals 14.2 Iteration of Double Integrals in Cartesian Coordinates | lecturing, discussing, problem solving |
10 | 14.4 Double Integrals in Polar 14.5 Triple Integrals 14.6 Change of Variables in Triple Integrals | lecturing, discussing, problem solving |
11 | 14.7 Applications of Multiple Integrals (The Surface Area of a Graph) Ch. 11: Vector Functions and Curves 11.1 Vector Functions of One Variable 11.3 Curves and Parametrizations | lecturing, discussing, problem solving |
12 | Ch. 15: Vector Fields 15.3 Line Integrals 15.1 Vector and Scalar Fields | lecturing, discussing, problem solving |
13 | 16.1 Gradient, Divergence, and Curl 15.2 Conservative Fields 15.4 Line Integrals of Vector Fields | lecturing, discussing, problem solving |
14 | 15.4 Line Integrals of Vector Fields Ch. 16: Vector Calculus 16.3 Green’s Theorem in the Plane | lecturing, discussing, problem solving |
15 | ||
16 | Final Exam |
Course Syllabus
# | Material / Resources | Information About Resources | Reference / Recommended Resources |
---|---|---|---|
1 | Robert A. Adams, Christopher Essex Calculus: A Complete Course, 7th Edition. | ||
2 | Stewart J. Calculus, 5th Edition | ||
3 | George B. Thomas Jr., Maurice D. Weir, Joel R. Hass Thomas’ Calculus, 12th Edition. |
Method of Assessment
# | Weight | Work Type | Work Title |
---|---|---|---|
1 | 40% | Mid-Term Exam | Mid-Term Exam |
2 | 60% | Final Exam | Final Exam |
Relationship between Learning Outcomes of Course and Program Outcomes
# | Learning Outcomes | Program Outcomes | Method of Assessment |
---|---|---|---|
1 | To effectively write mathematical solutions in a clear and concise manner. | 1͵7 | 1͵2 |
2 | To graphically and analytically synthesize and to apply multivariable and vector-valued functions and their derivatives, using correct notation and mathematical precision. | 1͵7 | 1͵2 |
3 | To use double, triple and line integrals in applications, including Green's Theorem. | 1͵7 | 1͵2 |
4 | To synthesize the key concepts of differential, integral and multivariate calculus. | 1͵7 | 1͵2 |
Work Load Details
# | Type of Work | Quantity | Time (Hour) | Work Load |
---|---|---|---|---|
1 | Course Duration | 14 | 4 | 56 |
2 | Course Duration Except Class (Preliminary Study, Enhancement) | 14 | 5 | 70 |
3 | Presentation and Seminar Preparation | 0 | 0 | 0 |
4 | Web Research, Library and Archival Work | 0 | 0 | 0 |
5 | Document/Information Listing | 0 | 0 | 0 |
6 | Workshop | 0 | 0 | 0 |
7 | Preparation for Midterm Exam | 1 | 8 | 8 |
8 | Midterm Exam | 1 | 2 | 2 |
9 | Quiz | 0 | 0 | 0 |
10 | Homework | 0 | 0 | 0 |
11 | Midterm Project | 0 | 0 | 0 |
12 | Midterm Exercise | 0 | 0 | 0 |
13 | Final Project | 0 | 0 | 0 |
14 | Final Exercise | 0 | 0 | 0 |
15 | Preparation for Final Exam | 1 | 12 | 12 |
16 | Final Exam | 1 | 2 | 2 |
150 |