Loyola University Chicago

John Felice Rome Center

MATH 161 Calculus I

Spring 2012


The main goal of this course is to provide a solid understanding of selected

topics in calculus of one variable and their applications. Conceptual and

computational skills will be developed, with an emphasis on understanding



A traditional introduction to differential and integral calculus. Functions,

limits, continuity, differentiation, intermediate and mean-value theorems,

curve sketching, optimization problems, related rates, definite and indefinite

integrals, fundamental theorem of calculus, logarithmic and exponential

functions. We will cover Chapters 1 through 5 (inclusive) from the textbook.


To provide students with the use of calculus on a variety of applications (e.g.

physics, economics and finance), and to provide students with the

background needed to enroll in Calculus II.


Calculus Early Trascendentals (Part 1), 12th edition (2009), by G. Thomas,

M Weir, J. Hass, Addison-Wesley Publisher, ISBN 0321628837,
















There will be 4 tests - each of them represents 15% of the final grade. The

final examination (comprehensive) is worth 30%, and 10% is represented by

assignments and class participation:

4 Tests...................................................60%

Final Exam ...........................................30%

Assignments and Class Participation ....10%


The grade scale is as follows:

A: 90%-100% (The student demonstrates complete, accurate, and critical knowledge of all the topics, is able to make

appropriate connections among different parts of the subject matter, uses the appropriate language and terminology

correctly and rigorously and is autonomous in his study)

B: 80%-89% (The student has a somewhat accurate knowledge of the subject matter and uses clear logic in his/her


C: 70%-79% (The student has the essential knowledge of the subject matter, understands the topics, and can express

it in a simple language)

D: 60%-69% (The student has a superficial, mnemonic knowledge of the subject matter, is uncertain and makes errors

in the presentations)

F: below 60% (At best, the students has a superficial knowledge of some of the topics discussed in the course. He

makes serious errors in the presentations).

Numerically, the final grade is computed as follows: G=0.15 T1 + 0.15 T2 + 0.15 T3 + 0.15 T4 + 0.3 F + 0.1 H,

where G is the final grade, T1 the score in the first test, T2 the score in the second test, T3 the score in the third

test, T4 the score in the fourth test, F the score in the final, H the average score in the homework and class

participation. The conversion between numerical grade and letter grade is described by the following table:

A 100 - 94

A- 93 - 90

B+ 89 - 87

B  86 - 83

B- 82 - 80

C+ 79 - 77

C  76 - 73

C- 72 - 70

D+ 69 - 67

D  66 - 63

D- 62 - 60

F  59 - 0






Cheating is not tolerated (please see the University Catalogue for the policy regarding

academic dishonesty).

Coming late to class or leaving early will be possible only with permission of the instructor.

No make-up exams will be given.


Attendance will contribute to the final grade. Full credit for attendance will be given to people

with two or fewer unexcused absences. Three or more absences will result with a proportional

reduction of the grade.


               Week 1: 1.1 Functions and their graphs. 1.2 Combining functions. 1.3 Trigonometric


               Week 2: 1.5 Exponential functions. 1.6 Inverse functions and logarithms. 2.1 Rates

                             change and tangent to curves.

               Week 3: TEST 1. 2.2 Limits of a function and limit laws. 2.3 The precise definition

                             of a limit. 2.4 One-sided limits.

               Week 4: 2.5 Continuity. 2.6 Limits involving infinity; Asymptotes of Graphs. 3.1

                             Tangent and derivative at a point.

               Week 5: 3.2 The derivative as a function. 3.3 Differentiation rules. 3.4 The derivative

                             as a rate of change.

               Week 6: TEST 2. 3.5 Derivatives of trigonometric functions. 3.6 The chain rule.


               Week 7: 3.7 Implicit differentiation. 3.8 Derivatives of inverse functions and

                            logarithms. 3.9 Inverse trigonometric functions.

               Week 8: 3.10 Related rates. 3.11 Linearization and differentials. TEST 3.

               Week 9: 4.1 Extreme values of functions. 4.2 The mean value theorem. 4.3

                             Monotonic functions and the first derivative test.

                Week 10: 4.4 Concavity and curve sketching. 4.5 Indeterminate forms and

                               L'Hopital rule. 4.6 Applied optimization. 4.7 Newton's method.  4.8  


               Week 11: 5.1 Area and estimating with finite sums. 5.2 Sigma notation and limits

                              of finite sums. TEST 4.

               Week 12: 5.3 The definite integral. 5.4 The fundamental theorem of calculus. 5.5

                              Indefinite integrals and the substitution method.

                Week 13: 5.6 Substitution and areas between curves. Review for final. FINAL.