Course Name Code Semester T+U Hours Credit ECTS
Mathematics II MAT 112 2 4 + 0 4 6
 Precondition Courses Recommended Optional Courses Course Language English Course Level Bachelor's Degree Course Type Compulsory Course Coordinator Öğr.Gör.Dr. EMİNE ÇELİK Course Lecturers Öğr.Gör.Dr. EMİNE ÇELİK, Course Assistants Teaching assistants of department of mathematics. Course Category General Training Course Objective To teach indefinite integral and methods, definition and properties of definite integrals,The funda,ental theorems of Calculus and related theorems, Applications of definte integrals (Calculation of Areas, arc lengths, volumes and surface areas), improper integrals and their propoerties, multi-variable functions. Course Content Indefinite integrals, techniques of integration, Properties of definite integrals, related theorems, applications of definite integration (areas between curves, volumes, arc lengths, area of a surface of a revolution.), Impropoer integrals and their properties, multi-variable functions.
# Course Learning Outcomes Teaching Methods Assessment Methods
1 (S)he evaluates areas and volumes using definite integrals Lecture, Testing, Homework,
2 (S)he recognizes the concept of the indefinite integral. Lecture, Problem Solving, Testing, Homework,
3 (S)he evaluates areas and volumes using improper integrals. Lecture, Testing,
4 (S)he evaluates arc lengths and areas of surfaces of revolution. Lecture, Testing, Homework,
5 (S)he calculates definite integral as a limit and finds definite integrals some special-type functions. Lecture, Problem Solving, Testing, Homework,
6 (S)he finds integrals of irrational functions. Lecture, Problem Solving, Testing, Homework,
7 (S)he evaluates integrals of rational functions. Lecture, Question-Answer, Problem Solving, Testing, Homework,
8 (S)he evaluates indefinite integrals via change of variables and integration by parts. Lecture, Problem Solving, Testing, Homework,
9 (S)he applies various substitution methods to evaluate indefinite integrals. Lecture, Problem Solving, Testing, Homework,
10 (S)he evaluates trigonometric integrals. Lecture, Problem Solving, Testing, Homework,
11 (S)he recognizes improper integrals and interprets their properties. Lecture, Problem Solving, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Indefinite integrals, basic integration rules, and the substitution rule.
2 Integration by parts. Integration of rational functions by partial fractions.
3 Trigonometric integrals. Trigonometric substitution.
4 Integral of some irrational functions. Binomial integral, and various substitution methods.
5 Areas, partitions. Riemann sums and definite integrals.
6 Evaluating definite integral as a limit. Proof of basic integration rules.
7 The fundamental theorem of calculus. The substitution rule for definite integral.
8 Integration by parts for definite integrals. Integration of some special-type functions.
9 Application of integration: Areas of regions between two curves.
10 Application of integration: Volume - The Disk Method.
11 Application of integration: Volume - The Shell Method.
12 Application of integration: Arc lengths and surfaces of revolution.
13 Improper Integrals.
14 Areas and volumes with improper integrals.
Resources
Course Notes <p>Lecture Notes</p>
Course Resources

[1] Thomas, G.B., Thomas` Calculus, 13e, Pearson Education, 2013.

[2] Larson, R., Edwards, B., Calculus, 11e, Cengage Learning, 2018.

[3] Stewart, J.  Calculus, 8e, Cengage Learning, 2016.

Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 70
1. Kısa Sınav 10
2. Kısa Sınav 10
3. Kısa Sınav 10
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
Course Duration (Including the exam week: 16x Total course hours) 16 4 64
Hours for off-the-classroom study (Pre-study, practice) 16 4 64
Mid-terms 1 10 10
Quiz 2 2 4
Assignment 1 10 10
Final examination 1 10 10
Total Workload 162
Total Workload / 25 (Hours) 6.48
dersAKTSKredisi 6