ADVANCED CALCULUS

Course Name Code Regular Semester ECTS Credits Credits Lecture 3 Application 0 Advanced Calculus 0252101 3 6 3 Laboratory (Hour/Week) 0

Course Language Turkish Compulsory or Elective Compulsory Equipment - Instructor Department of Mathematics Course Contents General Definitions; Definition of Differential Equation; Order and Solution Types; To Establish of Differential Equation; First Order Differential Equations; Separable, Homogeneous, Differential Equations Transforming Homogeneous Differential Equations and Solution Methods; First Order Linear Differential Equations; Bernoulli Differential Equation; Exact Differential Equation, Integrating Factors and Solution Methods; Clairaut, Lagrange, Riccati Differential Equations and Solution Methods; Second Order Differential Equations With One of the Variables Missing; Particular and General Solution Methods of Second Order Linear and Constant Coefficients Equations; nth Order Linear and Constant Coefficients Equations; Particular and General Solution Methods of Second Order Nonhomogeneous and Homogeneous Linear Equations; Solutions of Differential Equation with Operator Method Course Objectives To improve mathematical thinking to solve the problems which are met in mathematics, physics and engineering. Course Outcomes (The knowledge and the skills that the student will gain at the end of the course) To learn the all solution methods of differential equations which consist of functions of one variable. Textbook Course notes Additional References "Elementary Differential Equations and Boundary Value Problems", William E. Boyce - Richard C. Diprima, John-Wiley , 1992 "Diferansiyel Denklemler" volume 1 Prof. Yavuz Aksoy YTU, 1990

Prerequisite Courses - Prerequisite Subjects Derivative and Integral Homework/Project - Laboratory - Computer Applications - Additional Practices -

Course Evaluation Criteria Number Effective Proportion % Midterm Exams 2 60 Quiz - - Homework - - Term Projects - - Term Papers - - Laboratory - - Other - - Final Exam 1 40

Division of Course Credit (%) Basic Sciences 100% Basic Engineering and Departmental Core Courses -% Departmental Core Courses -% Social Sciences -%

WEEKLY COURSE PLAN

Week Subject 1 General Definitions; Definition of Differential Equation; Order and Solution Types; To Establish of Differential Equation 2 First Order Differential Equations; Separable, Homogeneous, Differential Equations Transforming Homogeneous Differential Equations and Solution Methods 3 First Order Linear Differential Equations; Bernoulli Differential Equation 4 Exact Differential Equation, Integrating Factors and Solution Methods 5 Clairaut, Lagrange, Riccati Differential Equations and Solution Methods 6 Second Order Differential Equations With One of the Variables Missing 7 Particular and General Solution Methods of Second Order Linear and Constant Coefficients Equations 8 1st midterm exam 9 Particular and General Solution Methods of Second Order Linear and Constant Coefficients Equations 10 Particular and General Solution Methods of Second Order Linear and Constant Coefficients Equations 11 nth Order Linear and Constant Coefficients Equations; Particular and General Solution Methods of Second Order Nonhomogeneous and Homogeneous Linear Equations 12 nth Order Linear and Constant Coefficients Equations; Particular and General Solution Methods of Second Order Nonhomogeneous and Homogeneous Linear Equations 13 2nd midterm exam 14 Solutions of Differential Equation with Operator Method 15 Solutions of Differential Equation with Operator Method

Prepared by Department of Mathematics Date 00.00.0000