Download SUBJECTS OF THE FINAL EXAMINATION THE SUBJECTS OF THE

MAT1031 CALCULUS I
10.01.2013
Dokuz Eylül University Faculty of Science Department of Mathematics
SUBJECTS OF THE FINAL EXAMINATION
Instructors: Engin Mermut and Celal Cem Sarıoğlu
Phones: (232) 301 85 82, 301 86 07
e-mails: [email protected]
and
[email protected]
web: http://kisi.deu.edu.tr/engin.mermut/ and http://kisi.deu.edu.tr/celalcem.sarioglu/
For announcements about the course, homeworks, results of your examinations, etc., see the
COURSE WEB PAGE:
http://kisi.deu.edu.tr/engin.mermut/MAT1031-Calculus-I-2012g.html
•
Textbook:
University Calculus, Early Transcendentals, Joel Hass, Maurice D. Weir, and George
B. Thomas, Jr., International Edition, 2nd edition, Pearson, 2012.
web page of the textbook for some supplements:
http://media.pearsoncmg.com/aw/aw_thomas_series_cw/tuc02/tuc02_student_launch.html
• GRADING:
Midterm
40%
Final Examination FINAL DATE: 18th January, 2013 Friday
Time: 13:00 Classrooms: B253, 254, 255, 256
60%
• SUGGESTIONS FOR FURTHER STUDY IN CALCULUS AND ANALYSIS.
This term we have seen one variable calculus: continuity, limits, derivative and integration of realvalued functions of a real variable. We have not given the proofs of all the properties of those. For a
rigorous presentation of all these, I suggest you to study the book Calculus by M. Spivak:
Spivak, Michael. Calculus. Corrected 3rd ed. Cambridge University Press, 2006.
This will be a very good preparation for your MAT 2043 Analysis I course next year, and will also be
useful for the Sequences and Series subject of our course MAT 1032 Calculus II next term.
If you want to learn the deeper properties of the concepts that you have learned this term, and if you
want to understand why the properties of limits, continuity, differentiation and integration are true
and if you want to learn the rigorous definitions and proofs of everything we have done this term, then
I recommend Spivak’s Calculus book that will teach you the background of this calculus work.
As a Turkish reference for the axiomatic construction of real numbers and for sequences and series
of real numbers and of functions, and for further topics in Analysis, study the below volumes of the
journal Matematik Dünyası.
•
MATEMATİK DÜNYASI
dergisinin 2007-III’ten itibaren olan sayıları gerçel sayılar,
diziler, seriler, süreklilik, limit, türev ve integral konularında çok faydalı olacaktır; Analiz (Calculus)
konusunda çıkmış olan ve bizim bu dönem ve gelecek dönem yapacağımız, ve gelecek de sene MAT2043
Analysis I ve MAT2044 Analysis II derslerinde yapacağınız bazı konuları kapsayan (ve daha sonraki bazı Analiz konusundaki seçmeli dersleriniz ile Topoloji konusuna giriş için faydalanabileceğiniz)
MATEMATİK DÜNYASI sayıları şunlardır: 2007-III Gerçel Sayılar I - Diziler (Sequences); 2007-IV
Gerçel Sayılar II - Diziler ve exp Fonksiyonu (Sequences and the exp Function); 2008-I Gerçel Sayılar
III - Diziler ve Seriler (Sequences and Series); 2008-II Gerçel Sayılar IV - Seriler (Series); 2008-III
Süreklilik ve Limit (Continuity and Limits); 2008-IV Düzgün Yakınsaklık (Uniform Convergence);
2009-I-II Topoloji (Topology); 2010-I Fonksiyonel Analiz (Functional Analysis)); 2010-II Türev (Differentiation); 2010-III Türev II - Fonksiyon Çizimi (Differentiation and Function Graphing); 2010-IV
Fonksiyon ve Eğri Çizimleri (Function and Curve Graphing); 2011-II İntegral (Integral); 2011-III
İntegral II (Integral II); 2011-IV İntegral III (Integral III); 2012-I Analizden Konular (Topics in Analysis); 2012-II Analizden Konular II (Topics in Analysis II); 2012-III İntegral IV (Integral IV); 2012-IV
Analizden Konular III (Topics in Analysis III).
→ See the next page for
THE SUBJECTS OF THE FINAL EXAMINATION.
•
SUBJECTS OF THE FINAL EXAMINATION.
All of the
first ten chapters of your textbook except Chapter 9, and some appendices of your textbook:
• Preliminaries: Real Numbers and The Real Line; Mathematical Induction; Theory of Real
Numbers; Complex Numbers; Lines, Circles and Parabolas; Conic Sections; Basic Algebra, Geometry and Trigonometry Formulas.
−→ Appendices A.1, A.2, A.3, A.4, A.7 and A.8.
• Functions: Functions and Their Graphs; Combining Functions, Shifting and Scaling Graphs;
Graphing with Calculators and Computers; Composition of Functions; Polynomial Functions;
Rational Functions; Algebraic Functions; Transcendental Functions; Trigonometric Functions;
Exponential Functions; Inverse Functions; Logarithms; Inverse Trigonometric Functions; Hyperbolic Functions; Inverse Hyperbolic Functions.
−→ All of Chapter 1 and Section 7.3.
• Limits and Continuity: Rates of Change and Tangents to Curves; Limit of a Function and
Limit Laws; Precise Definition of a Limit; Proofs of Limit Theorems; One-Sided Limits; Continuity; Limits Involving Infinity; Asymptotes of Graphs.
−→ All of Chapter 2 and Appendix A.5.
• Differentiation: Tangents and the Derivative at a Point; The Derivative as a Function; Differentiation Rules; The Derivative as a Rate of Change; Linearization and Differentials; Derivatives of
Trigonometric Functions; The Chain Rule; Implicit Differentiation; Derivatives of Inverse Functions and Logarithms; Derivatives of Inverse Trigonometric Functions; Derivatives of Hyperbolic
and Inverse Hyperbolic Functions; Related Rates.
−→ All of Chapter 3 and Section 7.3.
• Applications of Derivatives: Extreme Values of Functions; The Mean Value Theorem; Monotonic Functions and the First Derivative Test; Concavity and Curve Sketching; Indeterminate
Forms and L’Hôpital’s Rule; Proof of L’Hôpital’s Rule; Applied Optimization; Newton’s Method;
Antiderivatives.
−→ All of Chapter 4.
• Integration: Area and Estimating with Finite Sums; Sigma Notation and Limits of Finite
Sums; The Definite Integral; The Fundamental Theorem of Calculus; Indefinite Integrals and the
Substitution Rule; Substitution and Area Between Curves; The Logarithm Defined as an Integral;
Exponential Change and Separable Differential Equations; Hyperbolic Functions.
−→ All of Chapters 5 and 7
• Applications of Definite Integrals: Volumes Using Cross-Sections; Volumes Using Cylindrical Shells; Arc Length; Areas of Surfaces of Revolution; Work; Moments and Centers of Mass.
−→ All of Chapter 6.
• Techniques of Integration: Integration by Parts; Trigonometric Integrals; Trigonometric Substitutions; Integration of Rational Functions by Partial Fractions; Integral Tables and Computer
Algebra Systems; Numerical Integration; Improper Integrals.
−→ All of Chapter 8.
• Parametric Equations and Polar Coordinates: Parametrizations of Plane Curves; Calculus
with Parametric Curves; Polar Coordinates; Graphing in Polar Coordinates; Areas and Lengths
in Polar Coordinates; Conics in Polar Coordinates.
−→ All of Chapter 10.
• ANSWERS TO PROBLEMS. We have given the answers to the problems of your textbook.
Take a copy of the handwritten notes that Celal Cem Sarıoğlu has given; it contains some
summary and detailed solutions to many problems. These well written answers to the problems will
show you how you must write your answers in a mathematically correct way.
• EXAMINATIONS OF THE PREVIOUS THREE YEARS. We have given a copy of the
previous three years’ midterms and final examinations with detailed answers. Take a copy of these.
Make yourself a two and a half hour examination from these examinations. Then check the answers
to learn how you shall write your answers by making enough explanations.