Mathematical Methods for Physics
Exam Review
Course Introduction
This course provides a comprehensive introduction to the mathematical tools and techniques essential for advanced studies in physics. Topics include vector and tensor analysis, complex variables, ordinary and partial differential equations, Fourier and Laplace transforms, and special functions frequently encountered in physical applications. The course emphasizes not only the theoretical foundations but also practical problem-solving skills, enabling students to apply these mathematical methods to classical mechanics, electromagnetism, quantum mechanics, and other core areas of physics. Designed for physics majors and related disciplines, the course lays the groundwork necessary for both upper-level coursework and independent research.
Recommended Textbook
Calculus Concepts and Contexts Enhanced Edition 4th Edition by James Stewart
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93 Chapters
713 Verified Questions
713 Flashcards
Source URL: https://quizplus.com/study-set/3715 Page 2
Chapter 2: Extension G: Limits and Derivatives
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10 Verified Questions
10 Flashcards
Source URL: https://quizplus.com/quiz/74011
Sample Questions
Q1) A baseball diamond is a square with side 90 ft.A batter hits the ball and runs toward first base with a speed of 32 ft/s.At what rate is his distance from second base decreasing when he is halfway to first base? Round the result to the nearest hundredth.
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Chapter 2: Extension H: Limits and Derivatives
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5 Verified Questions
5 Flashcards
Source URL: https://quizplus.com/quiz/74012
Sample Questions
Q1) The circumference of a sphere was measured to be 88 cm with a possible error of 0.7 cm.Use differentials to estimate the maximum error in the calculated volume.
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4
Chapter 3: Extension F: Differentiation Rules
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5 Verified Questions
5 Flashcards
Source URL: https://quizplus.com/quiz/74018
Sample Questions
Q1) Find the value of the expression accurate to four decimal places. sinh 4
A) 29.3082
B) 55.5798
C) 15.145
D) 27.2899
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Chapter 4: Extension E: Applications of Differentiation
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12 Verified Questions
12 Flashcards
Source URL: https://quizplus.com/quiz/74024
Sample Questions
Q1) A piece of wire 10 m long is cut into two pieces.One piece is bent into a square and the other is bent into an equilateral triangle.How should the wire be cut for the square so that the total area enclosed is a minimum? Round your answer to the nearest hundredth.
A) 4.35 m
B) 3.25 m
C) 0 m
D) 5.35 m
E) 4.4 m
Q2) Find an equation of the line through the point (8,16) that cuts off the least area from the first quadrant.
Q3) The sum of two positive numbers is 16. What is the smallest possible value of the sum of their squares?
Q4) A farmer with 710 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle.What is the largest possible total area of the four pens?
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Chapter 4: Extension G: Applications of Differentiation
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12 Verified Questions
12 Flashcards
Source URL: https://quizplus.com/quiz/74026
Sample Questions
Q1) What constant acceleration is required to increase the speed of a car from 20 ft/s to 45 ft/s in 4 s?
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Chapter 7: Extension F: Differential Equations
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16 Verified Questions
16 Flashcards
Source URL: https://quizplus.com/quiz/74043
Sample Questions
Q1) Find the center of mass of the system comprising masses m<sub>k</sub> located at the points P<sub>k</sub> in a coordinate plane.Assume that mass is measured in grams and distance is measured in centimeters. m<sub>1</sub> = 3,m<sub>2</sub> = 4,m<sub>3</sub> = 5 P<sub>1 </sub>(-3,5),P<sub>2 </sub>(3,4),P<sub>3 </sub>(-4,1)
Q2) A trough has vertical ends that are equilateral triangles with sides of length 2 ft.If the trough is filled with water to a depth of 1 ft,find the force exerted by the water on one end of the trough.Round to one decimal place.(The weight density of water is 62.4 lb/ft<sup>3</sup>.)
A) 31.2 lb
B) 62.4 lb
C) 12.0 lb
D) 6.0 lb
Q3) An aquarium is 4 ft long,3 ft wide,and 2 ft deep.If the aquarium is filled with water,find the force exerted by the water (a)on the bottom of the aquarium,(b)on the longer side of the aquarium,and (c)on the shorter side of the aquarium.(The weight density of water is 62.4 lb/ft<sup>3</sup>.)
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8
Chapter 10: Extension A: Vector Functions
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9 Verified Questions
9 Flashcards
Source URL: https://quizplus.com/quiz/74058
Sample Questions
Q1) Find the standard equation of the sphere with center C and radius r. C (3,-5,3); r = 7
A) (x - 3)<sup>2</sup> + (y + 5)<sup>2</sup> + (z - 3)<sup>2</sup> = 49
B) (x - 3)<sup>2</sup> + (y + 5)<sup>2</sup> + (z - 3)<sup>2</sup> = 7
C) (x + 3)<sup>2</sup> + (y - 5)<sup>2</sup> + (z + 3)<sup>2</sup> = 49
D) (x + 3)<sup>2</sup> + (y - 5)<sup>2</sup> + (z + 3)<sup>2</sup> = 7
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9
Chapter 13: Extension E: Vector Calculus
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10 Verified Questions
10 Flashcards
Source URL: https://quizplus.com/quiz/74087
Sample Questions
Q1) Let f be a scalar field.Determine whether the expression is meaningful.If so,state whether the expression represents a scalar field or a vector field. curl f
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