General Information:
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- Instructor(s) Name: Paul Tsopméné
- Instructor(s) Email: paul.tsopmene@ubc.ca
- Duration: Term 2 Winter 2020 (Jan-Apr 2021)
- Delivery Modality: On Zoom. The link is posted on Canvas.
- Classroom Schedule: Tuesday: 9:30 AM – 11:00 AM, Wednesday: 11:30 AM – 1:00 PM
- Office Hours: Tuesday and Thursday: 2:15 PM – 3:15 PM. These will be held on Zoom. The link is posted on Canvas. I am also available by email or appointment if these times do not work for you.
- Course Website: Course materials are available on Canvas. My primary method of communication is through Canvas messages/emails. Make sure you check this website regularly.
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Course Objectives: To enable the student to:
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- Understand the fundamental concepts of integral calculus.
- Learn the most important techniques for calculating integrals.
- Practice how to apply these techniques to model and solve various problems including problems in Business and Economics.
- Gain some exposure to more advanced calculus concepts from a computational viewpoint as opposed to a full mathematically rigorous treatment.
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Course Overview: This course will focus on single and double variables integral calculus and its applications. While the list of topics aligns well with a general calculus course, most of the concepts will be presented through applications in Business and Economics. The course will start off with the concept of integration. In this chapter we will learn how to find indefinite and definite integrals using rules. We will also learn how to find the area between two curves and integrate numerically. In the second chapter, we will learn how to integrate using integration by parts, integrate by using tables, find improper integrals, and use integrals to find average values and solve continuous money flow problems. In the third chapter, we will learn how to use integrals to solve separable differential equations and linear first-order differential equations. In the fourth chapter, we will learn how to maximize or minimize a function of two variables. We will also learn how to find double integrals. In the last chapter, we will learn how to calculate probabilities for continuous random variables and find the expected value, variance, and standard deviation of a continuous random variable.
Contents: Topics include
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- Integration: Antiderivatives and Indefinite Integrals, Integration by Substitutions, Area and the Definite Integral, The Fundamental Theorem of Calculus, The Area Between Two Curves, Numerical Integration.
- Further Techniques and Applications of Integration: Integration by Parts, Integration Using Tables, Average Value, Continuous Money Flow, Improper Integrals.
- Differential Equations: Solutions of Elementary and Separable Differential Equations, Integrating Factors, Applications of Differential Equations.
- Multivariable Calculus: Functions of Several Variables, Partial Derivatives, Maxima and Minima, Lagrange Multipliers, Double Integrals.
- Probability and Calculus: Continuous Probability Models, Expected Value and Variance of Continuous Random Variables, Special Probability Density Functions (if time permits).
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Learning Outcomes: After completing this course, students will be able to:
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- Understand the basic idea of integral calculus: finding the area under a curve.
- Approximate the area under a curve by using the left, right, or midpoint Riemann sums.
- Evaluate integrals by using basic antiderivative formulas.
- Evaluate integrals by using techniques such as substitution and integration by parts.
- Use integrals to find the area between two curves, the cumulative/net change, and the average value of a function.
- Approximate the value of a definite integral using the midpoint rule, the trapezoidal rule, and Simpson’s rule.
- Determine whether an improper integral converges or diverges, and evaluate it if it is convergent.
- Use integrals to solve continuous money flow problems.
- Solve separable and first-order differential equations. Specifically, students should be able to: (1) Use integrals to solve separable differential equations and linear first-order differential equation. (2) Construct a differential equation modelling a quantity described in a problem.
- Find and interpret partial derivatives.
- Solve optimization problems involving several variables.
- Find double integrals.
- Calculate probabilities for continuous variables and find the expected values and the standard deviation.
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Learning Resources:
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- Textbook (Optional): Calculus with Applications, by Margaret L. Lial, Raymond N. Greenwell, and Nathan P. Ritchey, 11th edition, Pearson. This is optional, as the lecture contents and the practice problems I will post on Canvas will be enough.
- Practice Problems: Practice problems and detailed solutions as well as reviews of the relevant theories will be posted on Canvas every week. While completion of these problems is essential for the success in this course, you do not hand them in for grading.
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Course Outline: More information can be found in the course outline and the document titled “online test information’’.