one variable
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Topics include: Advanced memory management features of C and C++; the differences between imperative and object-oriented paradigms; the functional paradigm (using LISP) and concurrent programming (using C and C++); brief survey of other modern languages such as Python, Objective C, and C#. Prerequisites: Programming and problem solving at the Programming Abstractions level. Prospective students should know a reasonable amount of C++. Yo...more
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Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODEs) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especial...more
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Finding the volume when we have variable boundaries.
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Equations with the variable on both sides.
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U02_L1_T4_we1 : Example of solving for a variable.
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Expected value of a random variable.
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In this lecture, Professor Diamond continues her discussion of hematology by describing the two major blood cell types, erythrocytes and leukocytes. She begins by reviewing erythrocytes (red blood corpuscles or RBCs) and their characteristics. She discusses differences between RBC counts in men and women and factors like exercise that impact RBC counts. She then contrasts the properties of erythrocytes with those of leukocytes, noting t...more
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Introduction to basic physics of motion. Introduces the concept of variable velocity/acceleration.
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Solving linear equations with variable expressions in the denominators of fractions.
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This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space.
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Prroof that S (or entropy) is a valid state variable.
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Until now, the models we've used in this course have focused on the case where everyone can perfectly forecast future economic conditions. Clearly, to understand financial markets, we have to incorporate uncertainty into these models. The first half of this lecture continues reviewing the key statistical concepts that we'll need to be able to think seriously about uncertainty, including expectation, variance, and covariance. We apply these...more
