Course Details Language of Instruction English Level of Course Unit Bachelor's Degree Department / Program ELECTRICAL-ELECTRONICS E. Type of Program Formal Education Type of Course Unit Compulsory Course Delivery Method Face To Face Objectives of the Course Students completing this course will gain ability of 1. Using limit, continuity and differentiation concepts, 2. Sketching the graph of a function using asymptotes, critical points and the derivative test for increasing/decreasing and concavity properties, 3. Setting up and solving max/min problems, 4. Evaluating and applying integrals by using the Fundamental Theorem of Calculus, 5. Using indefinite integration technics. Course Content Functions: Functions and Their Graphs, Trigonometric Functions Limits and Contiunity: Rates of Change and Tangents to Curves, Limit of a Function and Limit Laws, The Sandwich (The Squeeze theorem), The Precise Definition of a Limit, One-sided Limits, Contiunity, Types of Discontiunity, Continuous Functions, The İntermediate Value Theorem, Limits İnvolving İnfinity, Asymptotes of Graphs, Differentiation: Tangents ,Normal Lines , The Derivative at a Point, The Derivate as a Function, Differentiable on an İnterval, One-sided Derivatives, Differentiation Rules, High order Derivatives, The Derivative as a Rate of Change, Derivatives of Trigonometric Fnctions, The chain rule, Implicit Differentiation, Linearization and Differentials, Applications of derivatives: Extrem Values of Functions, Critical Points, Rolle’s Theorem, The Mean Value Theorem, Monotonic Functions and The First Derivative Test: Increasing Functions and Decrasing Functions, the First Derivative Test for Local Extrema,Concavity and Curve Sketching, The Second Derivative Test for Concavity, Point of İnflection The Second Derivative Test for Local Extrema, Graphing of y=f(x), Antiderivatives, Indefinite İntegrals, Integration: Area and Estimating with Finite Sums, Average Value of Nonnegative Continuous Functions, Sigma Notation and Limits of Finite Sums, Riemann Sums, Definite İntegral, Properties of Definite İntegral, AreaUnder the Graph of a nonnegative Function, Average Value of Continuous Functions, Mean Value Theorem fo Definite İntegrals, The Fundamental Theorem of Calculus: Fundamental Theorem Part 1, Fundamental Theorem Part 2, Total Area, Indefinite İntegrals and the Substitution Method, Substitution and Area Between Curves, Integration with Respect to y, Definite İntegrals Of Symmetric Functions, Applications of Definite İntegrals: Volumes Using Cross-sections, The Disk Method, the Washer Method, The Ccylindrical Shell method, Arch Length, Areas of Surfuces of Revolution, Transcendental Functions:Inverse Functions and Their Derivatives, Natural Logarithms, Logarithms Functions and Their Derivatives, Logarithmic Differentiation, Integrals of Trigonometric Functions, Exponential Functions and Their Derivatives, Indeterminate Forms and L’Hospitals Rule, Cauchy’s Mean Value Theorem, Inverse Trigonometric Functions and Their Derivatives, Hyperbolic Functions and Their Derivatives,Inverse Hyperbolic Functions and Their Derivatives, Inverse Trigonometric Functions and Their Derivatives, Hyperbolic Functions and Their Derivatives,Inverse Hyperbolic Functions and Their Derivatives, Techniques of Integration: Integration by Parts, Integration by Parts Formula for Definite Integrals, Trigonometric Integrals, Reduction Formulas, Trigonometrik Substitutions, Integrations of Rational Functions by Partial Fractions, Improper Integrals: Improper Integrals of Type I and Type II Course Methods and Techniques Prerequisites and co-requisities None Course Coordinator None Name of Lecturers Associate Prof.Dr. Mehmet Şahin Assistants None Work Placement(s) No Recommended or Required Reading Resources Thomas’ Calculus (Twelfth Edition) by George B.Thomas ,Maurice D. Weir and Joel R.Hass. Course Notes Thomas’ Calculus (Twelfth Edition) by George B.Thomas ,Maurice D. Weir and Joel R.Hass. Documents Thomas’ Calculus (Twelfth Edition) by George B.Thomas ,Maurice D. Weir and Joel R.Hass Assignments - Exams Ders notları ve kaynak kitaplardan yapılır Course Category Mathematics and Basic Sciences %50 Engineering %50

 
 
 
 
  
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