Last update: 5/9/2007

Math 101 - Calculus I

 Homework 5 has been assigned; due on 05/12!
Solutions to Homework 4
Important announcements are to be placed here. Check often to be informed!
Check the course policy before asking any questions!
Midterm II is to be held on April 30, 2011, Saturday at 12:30 (Note the time change!)
Room assignment is according to your last/first name in the English lexicographic order
Using a wrong room will result in a penalty!!!
Midterm I solutions Midterm II solutions
Course home page: http://www.fen.bilkent.edu.tr/~gurses/math101.html. Check for homeworks, suggested problems, etc.
[Top]     [Home]             Instructor: Alex Degtyarev     Office: SA 130     Phone: x2135     Mail: degt-nospam-fen.bilkent.edu.tr
 Syllabus*   Spring 2001   Spring 2003   Spring 2006 
 [PDF]  Midterm I   MT I **  MT I **  MT I
 [PDF]  Midterm II   MT II **  MT II **  MT II
 [PDF]  Final   Final **  Final **  Final
 More stuff:    -Course contents
-Integrals
-Integration techniques
-Transcendental functions
   
  • Course policy [new]
  • Quiz & midterm results [new]
  • Homework (Set 1/Solutions; Set 2/Solutions; Set 3/Solutions; Set 4/Solutions; Set 5)
  • Suggested problems for self-study [updated]
  • Okan Tekman's Calculus 101 page
  • Metin Gurses' Calculus 101 page [new]
  • Exam rules and terms - Quizzes - Make-ups
    • * The files are in .pdf format. Download Acrobat Reader here. Postscript or .dvi files are available upon request
    ** The course used to be much more advanced. (Well, even nostalgia isn't what it used to be...) Thus, should you decide to work with the samples, stick to the topics listed below.
    Please disregard any crossed-out text. These subjects have not been decided upon yet.
    Especially this concerns the exam contents!
    Week  Topic  Notes
    1    Limits and Continuity (P, 2.1--2.3)   
    2    Limits and Continuity (continued; 2.4--2.6)   
    3    Derivatives (3.1--3.4)   
    4    Derivatives (continued; 3.5--3.10)      
    5    Extreme values and graphs (4.1--4.4)      
    6    Optimization (4.5)    Midterm I 
    7    L'Hôpital's rule (4.6); Indefinite integrals (4.8)   
    8    Definite integrals (5.1--5.3)   
    9    Fundamental theorems (5.4--5.6)  
    10    Applications of integration (6.1--6.6)   
    11    Applications of integration (cntd); Transcendental functions (7.1--7.3)    
    12    Transcendental functions (cntd; 7.4)   Midterm II  
    13    Techniques of integration (8.1--8.3)   
    14    Techniques of integration (cntd; 8.4--8.5);   
    15    Review   
        Finals week  Final  
    * These topics are likely to be skipped
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    Midterm I     (25%)   March 12, 2011, @ 12:30 pm       See   important remarks and room assignment

    Topics covered (tentative):          PDF Files: [MT I]  
  • Limits, continuous functions [problems]
  • Derivatives
  • Techniques of differentiation [problems]
  • Tangent lines [problems]
  • Simple applications (derivative as rate of change, related rates [problems], absolute extrema on closed intervals [problems])
  • The mean value theorem for derivatives [problems]

    Chapters:     2(1--7), 3(1--8), 4(1).
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    Midterm II     (25%)   April 30, 2011, @ 12:30 pm       See   important remarks and room assignment

    Topics covered (tentative):        PDF Files:  [CONTENTS]  [INTEGRALS]  [INTEGRATION]   (updated 4/10/2007)
  • Graphing functions using derivatives (critical points, increasing/decreasing, maxima and minima, concavity, points of inflection); asymptotes and dominant terms [problems]
  • Optimization problems [problems]
  • L'Hôpital's rule [problems]
  • Linearization, differential
  • Anti-derivatives; uniqueness; indefinite integrals; simple integration (using the basic rules/formulas and substitution) [problems]
  • Riemann sums and definite integrals; computing limits using integrals
  • The fundamental theorems of integral calculus and their applications (evaluating definite integrals; differentiating an integral with respect to its limits) [problems]
  • Applications of definite integrals: the basic idea*; areas between curves [problems]; arc length [problems]; volumes by slicing; volumes of solids of revolution (via disks and shells) [problems]; areas of surfaces of revolution; work; fluid forces; mass, moments, centers of gravity
  • Integration techniques: table integrals, substitution [problems], integration by parts [problems], integrals of rational functions (via partial fractions), trigonometric integrals, trigonometric/hyperbolic substitutions** [problems]
    * You are supposed to be able to set up the integral provided that the corresponding `naïve' laws are given
     ** Strictly speaking, trigonometric/hyperbolic substitutions reduce an integral with radicals to an integral of a trigonometric/hyperbolic expression. The latter reduces to an integral of a rational function, which we did not consider in general. Thus, you should expect that a proper substitution would result in a relatively simple integral!

    Chapters:     4(2--6, 8), 5(1--6), 6(1--4), 7(1), 8(1--4)
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    Final     (40%)   May 16, 2007, 12:15 pm     See   important remarks and room assignment

    Topics covered* (tentative):        PDF Files:  [CONTENTS]  [INTEGRATION]  [TRANSCENDENTAL FUNCTIONS]   (updated 5/9/2007)
  • Applications of definite integrals: the basic idea*; areas between curves [problems]; arc length [problems]; volumes; volumes of solids of revolution [problems]; areas of surfaces of revolution
  • Transcendental functions (exponential and logarithmic functions, inverse trigonometric functions, hyperbolic functions; you are supposed to know: definitions, algebraic identities, derivatives and integrals, applications to differentiation and integration) [problems]
    * The material of both midterms is fully included. The main emphasis of the course and, hence, the final is still differentiation, integration, and their applications!

    Chapters:     6 (1--2, 3, 5), 7 (1--4, 7, 8), 8 (1--5).
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    Quizzes and Homeworks     (10%)   Quizzes are to be held weekly on Tuesday in class (10-15 mins at the end) except midterm weeks. Hopefully, 8 to 9 quizzes and 3 homeworks will be given, with disregarding the two worst.
    Homeworks may be assigned 2 to 3 weeks prior each exam and are due before the exam. Only one randomly chosen question will be graded in each homework set. Thus, do them all to make sure that you get credit.

    All questions regarding the quizzes are to be directed to the assistant. The assistant is instructed to  give no credit  to identical papers. The same applies to the exams.

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    Make-ups    

    One common make-up (for all exams) will be given at the end of semester. If you have a good reason to request a make-up, just let me know. All supporting documents are to be taken to the math department secretary.

    No make-ups for quizzes!   If you have missed a lot of quizzes, it does affect your grade badly, and you have a  really good  reason for your absence, this can be settled personally at the end of the semester.
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    Remarks    

    Most exam problems will be taken from the textbook or its     web page. Solve them in advance, and you will do well!
    During the exams please keep in mind the following:
  • Calculators are  not  allowed 
  • Identical solutions (especially identically wrong ones) will  not  get credit. I reserve the right to decide what "identical" means. You still have the right to complain 
  • Do not argue about the distribution of the credits among different parts of a problem. I only accept complaints concerning my misunderstanding/misreadung your solution 
  • Show all your work. Correct answers without sufficient explanation might  not  get full credit 
  • Indicate clearly and unambiguously your final result. In proofs, state explicitly each claim 
  • Do not misread the questions or skip parts thereof. If you did, do not complain 
  • If you believe that a problem is misstated, do not try to solve it; explain your point of view instead. However, do not take advantage of this option: usually problems are stated correctly! 
  • Each problem has a reasonably short solution. If your calculation gets completely out of hand, something must be wrong (e.g., you might have chosen a wrong coordinate system/substitution/approach etc.) 

    Grading policy     *
    I will take off a few (2-3) points for arithmetical mistakes. However,  a lot  of points will be taken off for `obvious' mistakes, i.e., either those that you can easily avoid or those showing a deep misunderstanding of the subject. This includes, but is not limited to, the following:
  • Wrong dimension in a physical problem
  • Things that don't make sense
  • Mismatch of the data obtained in a graph (say, the only minimum of a continuous function lies above the only maximum, or function is concave up at a point of maximum, etc.)
  • Negative values for integrals of positive functions or for things like area, volume, mass, etc.
    Furthermore, solving a different problem (other than stated), even if perfect, will give you  no credit 
    * Of course, this only applies to problems that I am grading personally
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