LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS

AIM

1. To provide the methods of solution of systems of linear equations and the applications of matrix and determinant. 2. To introduce the basic concepts required to understand, construct, solve and interpret differential equations and to teach methods to solve differential equations of various types. 3. To give an ability to apply knowledge of mathematics on engineering problems

CONTENT

This course contains; Matrices and Systems of Linear Equations,Matrices and Systems of Linear Equations,Determinants,Vector Spaces,Vector Spaces,Eigenvalues and Eigenvectors,Eigenvalues and Eigenvectors,First order differential equations,First order differential equations,Higher order differential equations,Higher order differential equations,Higher order differential equations,Laplace Transform,Laplace Transform.

1. 1

   5. Solve higher order linear differential equations with constant coefficients and construct all solutions from the linearly independent solutions ; solve initial value problems using the Laplace transform

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

2. 2

   4. Solve first order linear equations and nonlinear equations of certain types , interpret the solutions and understand the conditions for the existence and uniqueness of solutions for linear differential equations

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

3. 3

   3. Classify differential equations according to certain features

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

4. 4

   2. Learn the importance of the concepts of vector space, basis and dimension and evaluate the eigenvalues and the corresponding eigenvectors of the matrix.

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

5. 5

   1. Solve the systems of linear equations, provide arithmetic operations with matrices, compute the inverse of matrix, determine the value of determinant of a matrix and use Cramer rule to solve the systems

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

WEEKLY PLAN

1. WEEK 1

   Matrices and Systems of Linear Equations

2. WEEK 2

   Matrices and Systems of Linear Equations

3. WEEK 3

   Determinants

4. WEEK 4

   Vector Spaces

5. WEEK 5

   Vector Spaces

6. WEEK 6

   Eigenvalues and Eigenvectors

7. WEEK 7

   Eigenvalues and Eigenvectors

8. WEEK 8

   First order differential equations

9. WEEK 9

   First order differential equations

10. WEEK 10

    Higher order differential equations

11. WEEK 11

    Higher order differential equations

12. WEEK 12

    Higher order differential equations

13. WEEK 13

    Laplace Transform

14. WEEK 14

    Laplace Transform

ASSESSMENT

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

WORKLOAD

READING

• Differential Equations & Linear Algebra Third Edition Edition, C.Henry Edwards ; David E. Penney Pearson International Education International,2011.

TEACHING STAFF

• Assist.Prof. Cihan Bilge GÜRBÜZCOORDINATOR
• Assist.Prof. Cihan Bilge GÜRBÜZ