CALCULUS III

AIM

1. To provide the concepts of polar coordinates and limit, continuity, integral of vector valued functions 2. To provide the applications of multiple integrals 3. To compute the line integrals and surface integrals and apply Green’s theorem, Stokes Theorem and Divergence Theorem

CONTENT

This course contains; Vector Valued Functions; Derivatives and Integrals of Vector Functions (T,N,B vectors),Directional Derivatives and the Gradient Vector,Maxima and Minima in Several Variables, Extrema of Functions,Lagrange Multipliers, Vector Fields,Line Integrals, Green's Theorem,Curl and Divergence,Parametric Surfaces and their Areas,Stoke's Theorem and Summary of Vector Calculus,Two Null Identities, Field Classification and Helmholtz's Theorem,Introduction to Electrostatic in Free Space and Coulomb's Law,Gauss Law and Applications, Electric Potential, Material Media in Static Electric Field,Flux Density, and Dielectric Constant,Electric Flux Density and Dielectric Constant ,Capacitance and Capacitors and Electrostatic Energy and Forces.

1. 1

   Compute the standard representation of a vector in 3-space, compute the dot product and cross product of vectors; write equations of lines, planes and quadric surfaces in 3-space.

   Taught by: Problem Solving Method, Self Study Method, Lecture Method · Assessed by: Traditional Written Exam, Homework

2. 2

   Use the concepts of continuity, differentiation, and integration of vector-valued functions.

   Taught by: Problem Solving Method, Self Study Method, Lecture Method · Assessed by: Traditional Written Exam, Homework

3. 3

   Compute multiple integrals over rectangular coordinates, nonrectangular coordinates and in other coordinate systems; apply multiple integrals in problems involving area, volume and surface area

   Taught by: Problem Solving Method, Self Study Method, Lecture Method · Assessed by: Traditional Written Exam, Homework

4. 4

   Compute line integrals and surface integrals and apply Green’s Green’s theorem, Stokes Theorem and Divergence Theorem

   Taught by: Problem Solving Method, Self Study Method, Lecture Method · Assessed by: Traditional Written Exam, Homework

5. 5

   Understanding of electrostatic in free space

   Taught by: Problem Solving Method, Self Study Method, Lecture Method · Assessed by: Traditional Written Exam, Homework

6. 6

   Understanding of electric flux and its relation with dielectric constant

   Taught by: Problem Solving Method, Self Study Method, Lecture Method · Assessed by: Traditional Written Exam, Homework

7. 7

   Understanding of electrostatic energy and its storage via capacitors

   Taught by: Problem Solving Method, Self Study Method, Lecture Method · Assessed by: Traditional Written Exam, Homework

WEEKLY PLAN

1. WEEK 1

   Vector Valued Functions; Derivatives and Integrals of Vector Functions (T,N,B vectors)

2. WEEK 2

   Directional Derivatives and the Gradient Vector

3. WEEK 3

   Maxima and Minima in Several Variables, Extrema of Functions

4. WEEK 4

   Lagrange Multipliers, Vector Fields

5. WEEK 5

   Line Integrals, Green's Theorem

6. WEEK 6

   Curl and Divergence

7. WEEK 7

   Parametric Surfaces and their Areas

8. WEEK 8

   Stoke's Theorem and Summary of Vector Calculus

9. WEEK 9

   Two Null Identities, Field Classification and Helmholtz's Theorem

10. WEEK 10

    Introduction to Electrostatic in Free Space and Coulomb's Law

11. WEEK 11

    Gauss Law and Applications, Electric Potential, Material Media in Static Electric Field

12. WEEK 12

    Flux Density, and Dielectric Constant

13. WEEK 13

    Electric Flux Density and Dielectric Constant

14. WEEK 14

    Capacitance and Capacitors and Electrostatic Energy and Forces

ASSESSMENT

• Rate of Midterm Exam to Success30%
• Rate of Final Exam to Success70%

WORKLOAD

READING

• Thomas’ Calculus, 12th Edition, G.B Thomas, R. L. Finney, M.D.Weir, F.R.Giordano, Addison
• 1. Fundamentals of Engineering Electromagnetics by David Cheng, First edition (main text for Electromagnetism) 2. Vector Calculus, 4th edition, Susan Jane Colley, Pearson edn.

TEACHING STAFF

• Assoc.Prof. Hüseyin Şerif SAVCICOORDINATOR
• Prof.Dr. İlteriş DEMİRKIRAN