MATA35H3

Calculus II for Biological Sciences

University of Toronto Scarborough

A calculus course emphasizing examples and applications in the biological and environmental sciences. Discrete probability; basic statistics: hypothesis testing, distribution analysis. Basic calculus: extrema, growth rates, diffusion rates; techniques of integration; differential equations; population dynamics; vectors and matrices in 2 and 3 dimensions; genetics applications.Note: This course will not satisfy the Mathematics requirements for any Program in Computer and Mathematical Sciences, nor will it normally serve as a prerequisite for further courses in Mathematics. Students who are not sure which Calculus II course they should choose are encouraged to consult with the supervisor(s) of Programs in their area(s) of interest.
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MATA35H3 Syllabus for Natalia Breuss — Spring 2019

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Department of Computer and Mathematical Sciences
Calculus I For the Life Sciences
MATA35 - Winter 2018
LECTURE (LEC01):
Monday 8:00- 10:00 Room: SY110
Thursday 8:00- 9:00 Room: SY110
INSTRUCTOR: Dr. N. Breuss Email: n.breuss@utoronto.ca
OFFICE HOURS: Wednesday 9:00-12:00 Room: IC484
MARKING SCHEME:
Hand in Assignments (5x2%) 10%
Quizzes (5x4%) 20%
Mid Term Test 30%
Final Exam 40%
--------------------------------------------------------
Total 100%
ASSIGNMENTS:
There will be eleven assignments posted on the course portal every week. Five assignments (all odd
numbered assignments) are hand-in assignments.
Your TA will mark the assignments and return them during the next tutorial. Each assignment is worth
2%, so together all hand-in assignments are worth 10%.
These assignments are your main resources for preparation for the quizzes and tests.
You can get help form TAs and instructors during their office hours or/and in the Math Centre (IC404,
AC312) to understand the assignment better.
TUTORIALS
During the tutorials students will be working on problems from assignments and discuss them with your TA
and your classmates
QUIZZES:
There will be five quizzes to be written in the tutorials. Each quiz is worth 4%, so together all quizzes are
worth 20%.
The quizzes will be based on the given assignments. There are no make-up quizzes. Zero mark will be
recorded for each missed quiz if a valid doctor note is not provided. Your TA will excuse the missed quiz if
the doctor note is presented to the TA in the next tutorial.
Department of Computer and Mathematical Sciences
MID-TERM TEST:
There will be one term test. It is worth 30%. Midterm test covers material from the assignments and lectures.
The exact day, time and location will be announced later in the course. Students who miss the midterm
without providing a valid doctor’s note will receive zero for the test.
FINAL EXAM:
The final exam will cover all topics discussed in the course. It is worth 40%.
COURSE PORTAL:
The course materials and assignments will be posted on Quercus. Students are advised to check the course
portal frequently. Assignments will be posted on Quercus by the end of each week.
COURSE REFERENCE:
The textbook for this course is Calculus for the Life Sciences, by Bittinger, Brandt and Quintanilla.
Publisher: Pearson Addison- Wesley. The text and the Student Solutions Manual can be purchased at the
UTSC bookstore.
Calculus I (MAT A29) covers five chapters from the textbook:
Chapter 5: Integration
Chapter 6: Matrices
Chapter 7: Functions of Several Variables
Chapter 8: First-Order Differential Equations.
Chapter 9: Higher-Order and System of Differential Equations.
THE MATH & STATS LEARNING CENTER:
Instructors, teaching assistants and other mathematics professors hold their office hours in the Math & Stat
Learning Centre (AC312) or in the Math Aid Room IC404. Feel free to come to either room with your math
questions. The schedule can be found at: http://ctl.utsc.utoronto.ca/mslc/
ACCESSIBILITY:
Students with diverse learning styles and needs are welcome in this course. In particular, if you have a
disability/health consideration that may require accommodations, please feel free to approach the
AccessAbility Service (located in SW302) as soon as possible. Inquiries are confidential. The UTSC
AccessAbility staff will assess your specific needs, provide referrals and arrange appropriate
accommodations. You can contact them at (416) 287-7560 or ability@utsc.utoronto.ca
CHEATING AND PLAGIARISM
Cheating and plagiarism are taken very seriously at the University of Toronto. Academic offences are treated
as a threat to the integrity of the institution as a whole and the penalties can be quite severe.
GENERAL REMARKS:
The following course outline for MATA35 is tentative; some material may be added or dropped as the
course develops. Any changes will be announced during regularly scheduled lecture hours and reflected in
the Course Outline.
MAT A35 ( Calculus for the Life Sciences II)
Course Outline
LW1. Preview. Integration. Techniques of Integration.
Techniques of Integration (Partial fractions decomposition and Integration by Parts)
LW2. Improper Integrals. Numerical Integration.
Application: Volumes, Areas.
Improper integrals (Type 1: Unbounded intervals. Type 2: Discontinuous integrand). Examples.
Application to Physics, Economics and Biology.
LW3. Matrices.
Matrix operations. Systems of linear equations. Applications: Leslie Diagram & Matrix.
Inverse matrix and cofactor expansions. Applications: Population models
LW4. Eigenvalues and Eigenvectors.
Computing Eigenvectors and Eigenvalues. Applications: Population Growth & Long Term
Growth Rate.
LW5. Functions of several Variables. Multiple integration.
Partial derivatives. Maximum minimum problems. Applications: Body Surface Area, Wind
Speed of Tornado, Optimization Problems.
LW6. Elements of Regression analysis.
Method of least squares. Best fit line. Quadratic, Exponential and Power dependences.
Application: Experimental Data Fitting (Project)
LW7. Separable and Linear First Order Differential Equations.
Pure time and autonomous differential equations.
Integrals as General and Particular Solutions. Direction fields and solution curves. Phase line.
Substitution methods. Bernoulli equation. Applications: General population Model. Logistic
Model. Carrying Capacity of Population.
LW8. Differential equations and mathematical modeling
Mixture problems. One and Two -Compartment models. Applications: Pollution of Great Lakes,
Crop Yield, Mixing Chemicals.
LW9. Higher- Order Differential Equations. Numerical Solutions.
Second Order Differential Equations with constant Coefficients. Homogeneous and non-
homogeneous equations.
Applications: Mechanical and Electrical Vibrations, Parallel Reactions.
LW10. Systems of Autonomous Differential Equations and Stability.
Autonomous Equations. Equilibrium Solution. Qualitative Analysis.
Applications: Logistic Growth Model with a Threshold, Crystallization, Decay Rate, Plant
Growth.
LW11. Power Series Expantion.
Taylor Series. Series representation of functions: linear and quadratic approximation.
Linearization.
LW12 Systems of Nonlinear Differential Equations.
Linearization. Applications: Population models. Predator-Prey & Coexistence of Species
equations.
Department of Computer and Mathematical Sciences
MAT A35 COURSE TIMETABLE (tentative)
Week/date
Sections in the textbook/
Assignments
Seminars (optional)
Week 1
(Jan 7-11)
Matrices
6.1-6.3
Assignment 1
Week 2
(Jan 1418)
Matrices
6.3-6.4
Assignment 2
Week 3
(Jan 21 25)
Functions of Several Variables
7.1-7.2
Assignment 3
Seminar:
Preparation for Q1
Week 4
(Jan 28-Feb 1)
Functions of Several Variables
7.3-7.4
Assignment 4
Week 5
(Feb 4 - 8)
Integration Techniques (Readings)
Assignment 5
Seminar:
Preparation for Q2
Week 6
(Feb 11 15)
First-Order Differential Equations
8.1-8.2
Assignment 6
Feb 18– 22
Reading Week
Week 7
(Feb 25 March 1)
First-Order Differential Equations
8.3-8.4
Assignment 7
Seminar:
Preparation for Q3
Week 8
(March 4 -8)
First-Order Differential Equations
8.5
Assignment 8
Week 9
(March 1115)
Systems of Differential Equations
9.1-9.3
Assignment 9
Seminar:
Preparation for Q4
Week 10
(March 18 22)
Systems of Differential Equations
9.4-9.6
Assignment 10
Week 11
(March 25 29)
Power Series (Readings)
Assignment 11
Seminar:
Preparation for Q5
Week 12
(April 1 – 5 )
Review

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