Math 121: Fall 2013 - Message: 11/23

Message from Professor Bozenna Pasik-Duncan: 11/23/13

Dear Students,

The content of the Math 121 course can be easily divided into 7 "mini-units":

General Knowledge of Functions, their descriptions, properties and different types.
Limits and Continuity.
Differentiability and Continuity.
Applications of Differentiation and Derivatives to Optimization Problems, Extrema, Monotonicity and Concavity of Functions.
Integrability, Differentiability and Continuity.
Definite, Indefinite and Improper Integrals with their Applications to Areas, Volumes, Arc Length and Average Values.
Real World Applications of Derivatives and Integrals to Science, Engineering and Probability.

The Summary of What we Need to Know for the Final Exam is the reflection of this devision into 7 "mini-courses".

Therefore, the following is what you are supposed to know not only for the Final Exam but also as the final result of your learning in this course.

Chapter 1: Functions, their Domains and Compositions.

1.3: Function Transformations – Examples: 6, 7, 8, 9.
1.6: Inverse Functions – Examples: 1, 2, 3, 9.

Chapter 2: Limits & Derivatives.

2.3: Finding Limits – Examples: 3, 4, 5, 6, 7, 8, 10.
2.4: Continuity – Examples: 2, 5, 6, 7, 9 (Intermediate Value Theorem).
2.5: Limits Involving Infinity – Examples: 4, 5, 6, 7, 8, 9.
2.6: Rates of Change – Examples: 3, 4, 5, 6.
2.7: Derivatives by the Definition and Higher Order Derivatives – Examples: 3, 9.
2.8: What do f' and f'' Say About f – Examples: 1, 3.

Chapter 3: Differentiation Rules, Tangent Lines, Velocity, Acceleration.

3.1: Derivatives of Polynomials and Exponential Functions – Examples: 5, 6, 7, 8, 9.
3.2 : The Product and Quotient Rules – Examples: 1, 2, 3, 5, 6.
3.3: Derivatives of Trigonometric Functions – Examples: 1, 3.
3.4: The Chain Rule – Examples: 1, 2, 3, 4, 6, 7, 8.
3.5: Implicit Differentiation – Examples: 1, 2, 3, 4.
3.6: Limits and Derivatives of Inverse Trigonometric Functions – Examples: 4, 5.
3.7: Derivatives of Logarithmic Functions and Logarithmic Differentiation – Examples: 1, 2, 3, 4, 5, 6, 7, 8.
3.8: Applications of Rates of Change – Examples: 1, 8.

Chapter 4: Applications of Differentiation.

4.1: Related Rates – Examples: 1, 2, 3, 4.
4.2: Maximum and Minimum Values – Examples: 1, 2, 3, 4, 5, 6, 7.
4.3: Derivatives and the Shapes of Curves – Examples: 2, 3, 4, 5, 6.
4.6: Optimization Problems – Examples: 1, 2, 3, 5, 6.
4.8: Antiderivatives – Examples: 1, 2, 3, 4, 5, 6.

Chapter 5: Integrals.

5.1: Areas – Example: 1.
5.2: The Definite Integral – Examples: 1, 2, 4, 5, 6, 7.
5.3: Evaluating Definite Integral – Examples: 1, 2, 3, 6.
5.4: The Fundamental Theorem of Calculus – Examples: 2, 3, 5.
5.5: The Substitution Rule – Examples: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
5.6: Integration by Parts – Examples: 1, 2, 3, 4, 5.
5.7: Additional Techniques of Integration – Examples: 4, 5.
5.9: Approximate Integration – Examples: 1.
5.10: Improper Integrals – Examples: 1, 2, 3, 4, 5, 6, 7, 8, 9.

Chapter 6: Applications of Integration.

6.1: Area Between Curves – Examples: 1, 2, 3, 5, 6.
6.2: Volumes – Examples: 1, 2, 3, 4, 5, 6.
6.3: Volumes by Cylindrical Shells – Examples: 1, 2, 3, 4.
6.4: Arc Length – Examples: 1, 2, 3, 4.
6.5: The Average Value of a Function – Examples: 1, 2, 3.

Applications: Sections 6.6, 6.7, 6.8 as Extra Credit.

6.6: Applications to Physics and Engineering – Examples: 1, 6.
6.6: Applications to Business and Biology – Examples: 1.
6.7: Applications to Probability – Examples: 1, 3, 4.

I hope that this will help you to review easily and with clear focus.

You have clear instructions for preparing well for the Final Exam. Make a goal to achieve good understanding of the above-listed concepts; with good understanding of all of them, I believe you will do well on the Final.

Review the Exams I and II as well as my Lecture Notes from November 8 - November 22 and December 2.

Then try the Sample Final Exam. The solutions to that sample will be posted later, after you have the opportunity to work on it by yourself or in groups.

Use the Peer Tutoring Program if you need quick help.

Enjoy the upcoming one-week break from lectures and lab meetings. You have the opportunity to use those meetings for your individual study. Thank you for your hard work.

Enjoy the Thanksgiving Holiday! Enjoy being with your Family and Friends!

I will see you on Monday, December 2.

With my very best wishes to each and everyone of you,

Bozenna Pasik-Duncan
Coordinator, Math 121' Fall 2013