Math 270 Week 1 Lab # 1
Topics: While the integral fills an area with an infinite number of rectangles and sums the areas to get an exact area under a curve, there are many methods for finding an approximate area under a curve as well. We will look at three methods, the first of which was already studied in Calculus I; Riemann Sums.
The other two methods are the Trapezoidal Rule and Simpson’s Rule. While Riemann Sums fill the area with rectangles, the Trapezoidal Rule fills the area with trapezoids, and Simpson’s Rule uses rectangular-like shapes but has parabolic ‘tops’. All three of these methods find the area of each geometric shape and adds them up to obtain the approximate area.
Math 270 Week 2 Lab # 2
Topics: Trigonometric Identities and powers of trigonometric functions, inverse trigonometric functions, integration by parts, trigonometric substitution, Partial Fraction decomposition, and integration using tables.
Math 270 Week 3 Lab # 3
Topics: Series, Operations, and Computations with Series, Maclaurin, Taylor
Math 270 Week 4 Lab # 4
Topics: The Taylor and Fourier Series are among the most important ideas in mathematics that you will encounter during this class. Please SHOW ALL YOUR WORK TO EARN FULL CREDIT as providing only answers will earn approximately 1/3 of the credit. Concepts include: Operations & Computations with Maclaurin, Taylor, and Fourier Series.
Math 270 Week 5 Lab # 5
Topics: Solutions of Diff. Eqns., Separation of Variables, 1st order Linear Diff. Eqns., Elementary applications. Please SHOW ALL WORK TO EARN FULL CREDIT as providing only an answer earns approximately 1/3 credit.
Math 270 Week 6 Lab # 6
Topics: Higher order homogeneous and non-homogeneous Differential Equations, with distinct, repeated, or complex roots
Math 270 Week 7 Lab #7
Topics: Laplace Transforms, one of the most useful transforms in all of mathematics. Because it allows us to move from the “differential” domain to an algebraic domain, operate algebraically to a solution, then transform back into equation space.