Advanced Calculus I-Vector Calculus
| Numbering Code | U-LAS10 20002 LE55 | Year/Term | 2022 ・ First semester |
|---|---|---|---|
| Number of Credits | 2 | Course Type | Lecture |
| Target Year | 2nd year students or above | Target Student | For science students |
| Language | English | Day/Period | Wed.5 |
| Instructor name | QURESHI，Ali Gul (Graduate School of Engineering Associate Professor) | ||
| Outline and Purpose of the Course | Based on the knowledge of Calculus with Exercises A/B and Linear Algebra with Exercises A/B , or Calculus A/ B and Liner Algebra A/B, this course explains calculus of multiple variables and vector calculus. The course introduces the concepts of motion and potential in more than 2 dimensions, which are based on partial differentiation and integration related with multiple dimensions (such as line integral and surface integral). | ||
| Course Goals | To learn basics of calculus in functions of two or more variables, which are used in many other courses in natural sciences (such as Physics) and engineering. | ||
| Schedule and Contents |
1. Basic operations with vectors (5 Weeks) - Dot and cross products; derivatives and integration of Vector Valued Functions 2. Vectors in other coordinate systems (2 Weeks) - Frenet-Serret frame, Spherical and Cylindrical coordinate systems 3. Vector fields and potentials at n-dimensional Euclidean spaces (2 weeks) - Operations over the vector fields (gradient, curl and divergence), scalar potential and vector potential 4. Line integrals and surface integrals (5 Weeks) - Line integrals at 2-dimensional plane, surface integrals at 3-dimensional space, and integral theorems (Divergence theorem of Gauss, the Green's formula and the Stokes's theorem) 5. Feedback（1 Week） |
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| Evaluation Methods and Policy | Weekly submission of class examples, class participation and homework (25%), Snap quizzes (25%), Final examination(50%) | ||
| Course Requirements | To understand Calculus with Exercises A/B and Linear Algebra with Exercises A/B, or Calculus A/B and Linear Algebra A/B. | ||
| Study outside of Class (preparation and review) | Students are encouraged to do assigned homework related to the classes. | ||
| References, etc. |
Calculus Vol. 3, Gilbert Srang et al., (Open Stax), Book is available online at https://openstax.org/details/books/calculus-volume-3 Thomas' Calculus, 14th ed., Joel R. Hass, Christopher E. Heil and Maurice D. Weir, (Pearson) Advanced Engineering Mathematics, 10th ed., Erwin Kreyszig, (Willey) Calculus, 6th ed., Frank Ayres Jr. and Elliott Mendelson, (McGraw-Hill) |
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