Math 148 Sections Fall 2018 Calculus II for Biological Sciences

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1 Math 148 Sections Fall 2018 Calculus II for Biological Sciences Instructor: Dr. Glenn Lahodny Jr. Teaching Assistant: Thomas Yahl Office: Blocker 211C thomasjyahl@math.tamu.edu Office Hours: MW 9:00 am 10:00 am or by appointment glahodny@math.tamu.edu Website: Meeting Time: TR 2:20 pm 3:35 pm Location: BLOC 149 Recitation Times and Locations: Section Meeting Time Location 501 MW 12:40 pm 1:30 pm FRAN MW 1:50 pm 2:40 pm BLOC MW 3:00 pm 3:50 pm BLOC 202 Textbook: Calculus for Biology and Medicine (3rd edition) by Claudia Neuhauser. Material to be Covered: Chapter 7 Integration Techniques Chapter 8 Differential Equations Chapter 9 Linear Algebra and Analytic Geometry Chapter 10 Multivariable Calculus Chapter 11 Systems of Differential Equations Catalog Description: Introduction to integral calculus in a context that emphasizes applications in the biological sciences; ordinary differential equations and analytical geometry. Prerequisite: MATH 147 or approval of instructor. Credit will not be given for more than one of MATH 148, MATH 152 and MATH 172. Learning Outcomes: This course is focused on quantitative literacy in mathematics with an emphasis on real world applications, especially to the biological sciences. Upon successful completion of this course, students will be able to: apply techniques for integration, including integration by parts and partial fraction decomposition. identify and compute improper integrals using limits. justify why an improper integral converges or diverges by applying the Comparison Theorem. approximate functions with Taylor polynomials and evaluate the error in the approximation by using the Taylor inequality. solve separable ordinary differential equations. understand how exponential population growth is modeled by a constant per capita growth rate while logistic population growth incorporates density dependence. 1

2 find equilibria of differential equations and analyze their stability both graphically and by using the stability criterion. apply various techniques for solving systems of equations, including Gaussian elimination. apply basic matrix algebra skills including addition, subtraction, scalar multiplication, and multiplication of matrices and find the inverse of a matrix and be able to use matrix algebra to solve problems. compute and interpret eigenvalues and eigenvectors for 2 2 matrices. use matrices in biological applications, including the study of age-structured populations. interpret 2 2 linear maps applied to 2 1 vectors. add, subtract, and scale vectors and compute dot products. use vectors in applications, including finding equations of lines and planes. understand concepts of limits and continuity for multivariable functions. use partial derivatives and linear approximations for solving real-world problems. understand and explain the concepts of equilibria and stability for biological systems of difference equations. correctly solve applied problems, and write the solutions in a coherent fashion. construct and analyze linear and nonlinear systems of differential equations applied in biology and medicine. Core Objectives Critical Thinking: The following critical thinking skills will be assessed on exams and other assignments. Students will: analyze integrals and determine the proper technique for integration, including integration by parts and partial fraction decomposition. identify and compute improper integrals using limits approximate functions with Taylor polynomials and evaluate the error in the approximation by using the Taylor inequality. solve separable ordinary differential equations. apply techniques for solving systems of equations, including Gaussian elimination. learn basic matrix algebra skills including addition, subtraction, scalar multiplication, and multiplication of matrices and be able to find the inverse of a matrix. creatively apply matrix algebra to solve systems of equations. compute and interpret eigenvalues and eigenvectors for 2 2 matrices. understand and apply concepts of limits and continuity for multivariable functions. 2

3 compute partial derivatives and linear approximations to solve real-world problems. compute equilibria and analyze their stability for biological systems of difference equations solve applied problems and write the solutions in a coherent fashion. analyze and construct linear and nonlinear systems of differential equations applied in biology and medicine. Communication Skills: The following communication skills will be assessed on exams and other assignments. Students will: justify why an improper integral converges or diverges by applying the Comparison Theorem. understand how exponential population growth is modeled by a constant per capita growth rate while logistic population growth incorporates density dependence. apply basic matrix algebra skills including addition, subtraction, scalar multiplication, and multiplication of matrices and finding the inverse of a matrix to solving problems. interpret the action of 2 2 linear maps applied to 2 1 vectors both graphically and numerically. add, subtract, and scale vectors and compute dot products. use vectors in applications, including finding equations of lines and planes. solve applied problems and write the solutions in a coherent fashion. construct and analyze linear and nonlinear systems of differential equations applied in biology and medicine. Empirical and Quantitative Skills: The following empirical and quantitative skills will be assessed on exams and other assignments. Students will: apply techniques for integration, including integration by parts and partial fraction decomposition. solve separable ordinary differential equations. compute and interpret eigenvalues and eigenvectors of 2 2 matrices. compute the Leslie matrix associated with a given data set pertaining to an age-structured population and use it to make predictions of population sizes for future generations. use partial derivatives and linear approximations for solving real-world problems. compute equilibria and analyze their stability for biological systems of difference equations. manipulate given information to construct and analyze linear and nonlinear systems of differential equations applied to biology and medicine. 3

4 Grading Policy: Students grades will be determined by their performance on weekly lab assignments, quizzes, exams, and a comprehensive final exam. Grade Distribution: A [90,100] Lab Assignments: 5% B [80,90) Quizzes: 10% C [70,80) Exams: 60% (Each exam is worth 20%) D [60,70) Final Exam: 25% F [0,60) Suggested Homework: Homework problems will be assigned from the textbook each week. These problems will not be collected for a grade. However, the weekly lab assignments and quizzes will include problems similar to the suggested homework problems. Lab Assignments: Weekly lab assignments will be administered during the recitation sessions. Students are allowed to work in small groups (2 or 3 students) to complete the assignments. Lab assignments will not be administered during the weeks of exams. Quizzes: Weekly quizzes will be administered during the recitation sessions. Students must work alone to complete the quizzes. Quizzes will not be administered during the weeks of exams. Exams: There will be three exams administered on the dates listed below. Exam 1: September Exam 2: October Exam 3: November Students with verified disabilities can make arrangements for the exam to be administered by the Office of Support Services for Students with Disabilities. Exam Format/Information: 1. Students need to bring a ScanTron (#815-E), a # 2 pencil, and their TAMU student ID to each common exam. 2. Each exam will consist of two parts: multiple-choice (no partial credit) and short answer (partial credit possible). 3. The multiple-choice part of the exam will be administered during recitation sessions. The short answer part of the exam will be administered during lecture. 4. Calculators or electronic devices of any other type are not permitted for any exam. 5. The entire exam is closed book. Students are not allowed to use notes or formula sheets. Final Exam: The final exam will be administered on December 12 from 1:00 3:00 pm. Material on the final exam will be similar to the examples presented in class, problems from the suggested homework, and problems from previous exams. A student s final exam grade will replace their lowest exam grade, provided that the final exam grade is greater. Make-Up Policy: Make-up work will only be allowed in the case of an excused absence as defined by TAMU Student Rule 7. In this case, appropriate documentation of the absence must be provided to the instructor. Wherever possible, students should inform the instructor before an absence. Consistent with TAMU Student Rule 7, students are required to notify an instructor by the end of the next working day after missing an assignment or exam. 4

5 Tentative Weekly Schedule: Week 1: Calculus review and integration by substitution. Section 7.1. Week 2: Integration by parts and partial fractions. Sections Week 3: Improper integrals and the Taylor approximation. Sections 7.4 and 7.6. Week 4: Separable differential equations, equilibria, and stability. Sections Week 5: Exam I (Covering , 7.6, ), linear systems, and matrices. Sections Week 6: Eigenvalues, eigenvectors, and vector algebra. Sections Week 7: Functions of several variables, limits, and continuity. Sections Week 8: Partial derivatives, tangent planes, differentiability, and linearization. Sections Week 9: Exam II (covering ), the gradient. Section Week 10: Optimization. Section Week 11: Systems of difference equations. Section Week 12: Linear systems and applications. Sections Week 13: Nonlinear autonomous systems. Section Week 14: Exam III (covering , ), applications of nonlinear systems. Section Week 15: Review for final exam. Important Dates: November 16 Last day to drop a course with no penalty (Q-drop) November Thanksgiving Holiday December 4 Last day of class December 12 Final Exam Extra Help: The Mathematics Department offers help sessions for students. These sessions are designed to help students with their homework problems and other questions. A schedule for help sessions can be found at Academic Integrity: Students in this course are allowed to discuss suggested homework problems and solutions. However, students are not permitted to copy homework solutions from another student. Students are not permitted to discuss any aspect of an exam until all students have completed the exam. The penalties for violating this policy will range from an F on an assignment or exam to failing the course. Always abide by the Aggie Code of Honor: An Aggie does not lie, cheat or steal, or tolerate those who do. For further information regarding academic integrity, please visit Americans with Disabilities Act (ADA): The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact Disability Services, in Cain Hall, Room B118, or call For additional information, please visit Students should present appropriate verification from Student Disability Services during the instructor s office hours. 5

Mathematics. Mathematics

Mathematics. Mathematics Mathematics Program Description Successful completion of this major will assure competence in mathematics through differential and integral calculus, providing an adequate background for employment in