Credit: (3-2)4 

Content: Analytic Geometry in R² , R³. Functions of one and several variables: Limit, continuity and differentiation. Chain rule, implicit differentiation. Differential calculus, optimization, Lagrange multipliers. The definite integral. The indefinite integral. Logarithmic and exponential functions. Techniques of integration: Integration by substitution, integration by parts, by partial fractions. 

Goals: Introduce the students to the methods of analytic geometry and vectors for studing curves and surfaces. Then a rapid study of calculus is made to sketch curves, to find extreme values of functions of a single and several variables and to evaluate areas between two curves through integration. 

Course Outline: 

• (Week 1) Coordinate systems in the plane and space. 
• Distance. Area of a triangle 
• (Week 1) Polar coordinates. Transformation of coordinates. 
• (Week 1) Curves and surfaces in space. Vectors. 
• (Week 1) Vectors. Lines and planes. 
• (Week 1) Functions, limits, continuity. 
• (Week 1) The derivative. The chain rule. 
• (Week 1) Partial derivatives. Approximations. 
• (Week 1) Absolute and local extrema. First and Second derivative tests. Asymptotes. 
• (Week 1) Curve sketching. Optimization problems. 
• (Week 1) Lagrange multipliers. 
• (Week 1) The definite integral. Areas between two curves. 
• (Week 1) The Fundamental Theorem. Logarithmic and exponential functions. 
• (Week 1) Integration by substitution and by parts. 
• (Week 1) Integration of rational functions. 

Suggested textbook: M.Dabbagh, A. Doğanaksoy; Basic Mathematics II, Middle East Technical University, Department of Mathematics, Ankara, 1995 
 
 
 

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