Single Variable Analysis II(MAT102)

Course Code Course Name Semester Theory Practice Lab Credit ECTS
MAT102 Single Variable Analysis II 2 5 0 0 5 7
Admission Requirements
Language of Instruction French
Course Type Compulsory
Course Level Bachelor Degree
Course Instructor(s) Ayşegül ULUS (Email)
Objective To build, with appropriate rigour, the foundations of calculus and along the way to develop the skills to enable us to continue studying mathematics
Content Course syllabus : Intermediate Value Theorem, Limit, Continuity, Trigonometric functions, Asymptotes, Differentiation, Mean Value Theorem, Rolle Theorem, L’Hospital Rule, Graphs of functions, Hyperbolic functions, Riemann integral- Darboux theorem, Area and volume calculation, Improper integral.
Course Learning Outcomes The student is expected to learn the main notions and the teorems (Intermediate Value Theorem, Differentiation, Mean Value Theorem, Rolle Theorem, Riemann integral, Improper integral). The student will be able make the applications and he/she will be able to draw the usual functions graphics
Teaching and Learning Methods Courses and the problem solving
References A First Course in Real Analysis, Sterling K.Berberian, Springer

Calculus, TÜBA yayınları

Mathématiques de 1er cycle, 1er année, Dixmier
Print the course contents
Theory Topics
Week Weekly Contents
1 Limit and continuity
2 Derivatives
3 Derivatability , l'Hopital Rule
4 Mean Value Theorem and Rolle Theorem
5 Derivative change, convex concave functions, asymptotes,
6 Graphs of Functions
7 Midterm Exam I
8 Taylor Theorem
9 Applications of Derivative
10 Integral and Primitive, Riemannian Integration
11 Theorem Combining Derivative and Integral for Continuous Functions: Fundamental Theorem of Calculus
12 Midterm exam II
13 Improper Integral
14 Applications of Integral
Practice Topics
Week Weekly Contents
Contribution to Overall Grade
  Number Contribution
Contribution of in-term studies to overall grade 2 60
Contribution of final exam to overall grade 1 40
Toplam 3 100
In-Term Studies
  Number Contribution
Midterm Examinations (including preparation) 2 60
Toplam 2 60
No Program Learning Outcomes Contribution
1 2 3 4 5
1 understands principles of deductive reasoning; has experience to verify well-foundedness and exactness of mathematical statements in systematic ways; X
2 can properly state and use concepts and results of major mathematical interest; X
3 masters current computational techniques and algorithms; has a good ability in their use; can identify relevant tools, among those one has learned, suitable to solve a problem and is able to judge whether or not one is in possession of these tools; X
4 is able to express one’s mathematical ideas in an organised way both in written and oral forms; X
5 understands relations connecting substantial concepts and results; can switch from one viewpoint to another on mathematical objects (pictures, formulae, precise statements, heuristic trials, list of examples,...); X
6 has followed individually a guided learning strategy; has pursued steps toward the resolution of unfamiliar problems; X
7 has a theoretical and practical knowledge in computer science well adapted for learning a programming language; X
8 has investigated the relevance of modeling and using mathematical tools in natural sciences and in the professional life; is conscious about historical development of mathematical notions; X
9 has followed introduction to some mathematical or non-mathematical disciplines after one’s proper choice; had experience to learn selected subjects according to one’s proper arrangement; X
10 masters French language as well as other foreign languages, to a level sufficient to study or work abroad. X
Activities Number Period Total Workload
Class Hours 14 5 70
Working Hours out of Class 14 5 70
Midterm Examinations (including preparation) 2 10 20
Final Examinations (including preparation) 1 10 10
Total Workload 170
Total Workload / 25 6,80
Credits ECTS 7
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