PRE-CALCULUS

AIM

The aim of this course is to introduce the real number line, interval notation, absolute value and methods for solving linear, polynomial, and rational inequalities, as well as to provide students with a comprehensive understanding of algebraic, exponential, logarithmic, trigonometric, and inverse trigonometric functions. Furthermore, students who successfully complete the course will develop the algebraic manipulation skills necessary for success in Calculus.

CONTENT

This course contains; Fundamental Concept of Algebra,Rectangular Coordinates and Analytic Geometry,Functions and Their Graphs,Functions and Their Graphs,Polynomials and Rational Functions,Polynomial and Rational Functions,Exponential and Logarithmic Functions ,Midterm Week,Trigonometry,Trigonometry,Analytic Trigonometry,Complex Numbers,Advance Problems for Calculus,Advance Calculus Problems.

1. 1

   1. Evaluate equations and inequalities involving absolute value, polynomial and retional expressions in real space.

   Taught by: Problem Solving Method, Self Study Method, Experiential Learning, Lecture Method · Assessed by: Multiple-Choice Exam

2. 2

   2. Interprets the graphs of lines, parabolas, ellipses, and hyperbolas in Cartesian coordinates.

   Taught by: Problem Solving Method, Self Study Method, Experiential Learning, Lecture Method · Assessed by: Multiple-Choice Exam

3. 3

   3. Analyze piecewise-defined and elementary functions, and their transformations (translations, reflections, and dilations) through both algebraic and graphical methods, applying these concepts to model and solve real-world problems involving complex functional structures.

   Taught by: Problem Solving Method, Self Study Method, Experiential Learning, Lecture Method · Assessed by: Multiple-Choice Exam

4. 4

   4. Evaluate exponential and logarithmic functions by investigating their properties and inverse relationships; analyze growth and decay processes.

   Taught by: Problem Solving Method, Self Study Method, Experiential Learning, Lecture Method · Assessed by: Multiple-Choice Exam

5. 5

   5. Investigate trigonometric and inverse functions using radian and degree measures; interpret their unit circle relationships, transformations, and identities to solve trigonometric equations through algebraic and graphical methods.

   Taught by: Problem Solving Method, Self Study Method, Experiential Learning, Lecture Method · Assessed by: Multiple-Choice Exam

6. 6

   6. Examine the relationship between the polar form of complex numbers and Euler’s formula; examine Euler’s formula to explore the algebraic connections and transitions between trigonometric and hyperbolic functions.

   Taught by: Problem Solving Method, Self Study Method, Experiential Learning, Lecture Method · Assessed by: Multiple-Choice Exam

WEEKLY PLAN

1. WEEK 1

   Fundamental Concept of Algebra

   Preparation: Book chapter-Appendix A1-A7

2. WEEK 2

   Rectangular Coordinates and Analytic Geometry

   Preparation: Book Chapter 1.1,1.2, 1.3, 10.1, 10.2, 10.3, 10.4

3. WEEK 3

   Functions and Their Graphs

   Preparation: Book Chapter 1.4, 1.5, 1.6, 1.7, 1.8, 1.9

4. WEEK 4

   Functions and Their Graphs

   Preparation: Book Chapter 1.4, 1.5, 1.6, 1.7, 1.8, 1.9

5. WEEK 5

   Polynomials and Rational Functions

   Preparation: Book Chapter 2.1, 2.2, 2.3, 2.5, 2.6

6. WEEK 6

   Polynomial and Rational Functions

   Preparation: Book Chapter 2.1, 2.2, 2.3, 2.5, 2.6

7. WEEK 7

   Exponential and Logarithmic Functions

   Preparation: Book chapter 3.1, 3.2, 3.3, 3.4

8. WEEK 8

   Midterm Week

9. WEEK 9

   Trigonometry

   Preparation: Book Chapter 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7

10. WEEK 10

    Trigonometry

    Preparation: Book Chapter 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7

11. WEEK 11

    Analytic Trigonometry

    Preparation: Book Chapter 5.1, 5.2, 5.3, 5.4, 5.5

12. WEEK 12

    Complex Numbers

13. WEEK 13

    Advance Problems for Calculus

    Preparation: Thomas Calculus

14. WEEK 14

    Advance Calculus Problems

    Preparation: Thomas Calculus

ASSESSMENT

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

READING

• Ron Larson 10th Edition
• Calculus Volume 1 – Edwin Jed Herman, Gilbert Strang, Calculus: A Complete Course – Robert Adams, Thomas Calculus 13th Edition.

TEACHING STAFF

• Assist.Prof. Özge BİÇER ÖDEMİŞCOORDINATOR
• Assist.Prof. Özge BİÇER ÖDEMİŞ
• Res.Assist. Recep Akif TAŞÇI