Advanced Mathematics

Course Code:

MATH 134

Course Period:

Spring

Course Type:

Core

P:

3

Application:

0

Credits:

3

ECTS:

5

Prerequisite Courses:

Basic Mathematics

Course Language:

İngilizce

Course Objectives:

Limits, compound interest, continuity. Derivative and rules of differentiation. Exponential and logarithmic functions. Extremal values, trends, elasticity of demands. Linear programming and multiple optimum solutions. Simplex method and optimization. Applications to compound interest, present value, annuities, amortization of loans. Applications to modeling in economics and business. Introduction to probability and statistics.

Course Methodology:

1: Lecture

Course Evaluation Methods:

A: Written examination

Vertical Tabs

Course Learning Outcomes

Learning Outcomes	Teaching Methods	Assessment Methods
1) Learns the foundational notions of Calculus: limit and continuity.	1	A
2) Learns the notion of derivative through limit, learns properties of derivation and the chain rule.	1	A
3) Learns implicit differentiation.	1	A
4) Learns sketching of curves in cartesian coordinates, can do extremum calculations. Learns the notion of concavity. Learns: 1st derivative test, 2nd derivative test and the applications of the notions maxima and minima	1	A
5) Solves compound interest questions and learns the notion of present value.	1	A
6) Learns basic counting techniques and can do elemantary probability and statistical calculations.	1	A

Course Flow

Week	Topics	Study Materials
1	Chapter 10: Limit and Continuity Limits	10.1, 10.2
2	Continuity	10.3
3	Chapter 11: Differentiation The Derivative, Rules of Differentiation	11.1, 11.2
4	The product rule and the Quotient rule, The chain rule	11.4, 11.5
5	Chapter 4: Exponential and Logarithmic Functions Exponential Functions, Logarithmic Functions	4.1, 4.2
6	Properties of Logarithms, Logarithmic and Exponential Equations	4.3, 4.4
7	Chapter 12: Additional Differentiation Topics Derivative of logarithmic functions, Derivatives of Exponential Functions	12.1, 12.2
8	Implicit Differentiation, Logarithmic Differentiation	12.4, 12.5
9	Chapter 13: Curve Sketching Relative Extreme Absolute Extrema on Closed Interval, Concavity	13.1, 13.2, 13.3
10	The Second Derivative Test, Asymptotes, Applied Maxima and Minima	13.4, 13.5, 13.6
11	Chapter 5: Mathematics of Finance Compound Interest, Present Value	5.1, 5.2, 5.4
12	Interest Compounded Continuously	5.3
13	Chapter 8: Introduction to Probability and Statistics Basic Counting Principle and Permutations, Combinations and Other Counting Principles	8.1, 8.2
14	Sample Spaces and Events, Probability	8.3, 8.4

Recommended Sources

Textbook	Introductory Mathematical Analysis, 13th Edition by Ernest Haeussler, Richard S. Paul, Richard Wood, Pearson Prentice Hall
Additional Resources

Assessment

IN-TERM STUDIES	NUMBER	PERCENTAGE
Mid-terms	1	100
Quizzes
Assignments
Total		100
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE		60
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE		40
Total		100

ECTS

Activities	Quantity	Duration (Hour)	Total Workload (Hour)
Course Duration (14x Total course hours)	14	3	42
Hours for off-the-classroom study (Pre-study, practice)	14	4	56
Mid-terms (Including self study)	1	12	12
Final examination (Including self study)	1	15	15
Total Work Load			125
Total Work Load / 25 (h)			5
ECTS Credit of the Course			5

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