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MATH 1081 (16)

All Educational Materials for MATH 1081 at University of Colorado - Boulder

Calculus for Social Science and Business

Textbook Guide Mathematics: Integral, Trigonometric Substitution, Trapezoidal Rule

Techniques of Integration 7.1 Integration by Parts Formula for integration by parts: Alternative notation: If we combine the formula for integration by parts with Part 2 of the Fundamental Theorem of Calculus, we can evalu...

Mathematics
MATH 1081
Textbook Guide Mathematics: Semi-Major And Semi-Minor Axes, Parametric Equation, Polar Regions Of Earth

Parametric Equations and Polar Coordinates 10.1 Curves Defined by Parametric Equations Suppose that x and y are both given as functions of a third variable t (called a parameter) by the equations x = f(t) and y = g(t) (cal...

Mathematics
MATH 1081
[MAT133] - Final Exam Guide - Everything you need to know! (197 pages long)

Functions and Models 1.1 Four ways to represent a function Representations of functions o A function f is a rule that assigns to each element x in a set D exactly one element, called f(x), in a set E. o The set D is called...

Mathematics
MATH 1081
Textbook Guide Mathematics: Frenet–Serret Formulas, Twisted Cubic, Trefoil Knot

Vector Functions 13.1 Vector Functions and Space Curves Learning Objectives Understanding vector functions and space curves Determining the continuity of vector functions Any function whose domain is a set of real numbers ...

Mathematics
MATH 1081
Textbook Guide Mathematics: Directional Derivative, Thermal Conduction, Tangent Space

Partial Derivatives Partial derivatives of functions are techniques for finding the derivatives of functions of two or more variables. They are normally applicable to certain real life phenomena of physical sciences which ...

Mathematics
MATH 1081
Textbook Guide Mathematics: Ibm System P, Scilab, Convergent Series

Infinite Sequences and Series 11.1 Sequences A sequence is an arrangement of numbers in a definite order. A sequence can be finite when it contains a finite numbers or it can be infinite when it contains infinite numbers. ...

Mathematics
MATH 1081
Textbook Guide Mathematics: Electrical Network, Damping Ratio

Secondorder differential equations 17.1 SecondOrder Linear Equations Forms: o A secondorder linear differential equation has the form o The form of a secondorder linear homogeneous differential equation is (Equation 2) Sol...

Mathematics
MATH 1081
Textbook Guide Mathematics: Carrying Capacity, Integrating Factor, Restoring Force

Differential Equations 9.1 Modeling with Differential Equations Models of Population Growth o Variables: t = time (the independent variable) P = the number of individuals in the population (the dependent variable) o Assump...

Mathematics
MATH 1081
Textbook Guide Mathematics: Antiderivative, If And Only If

Integrals 5.1 Areas and Distances The exact distance d traveled is the limit of such expressions 5.2 The Definite Integral Definition: Theorems: Evaluating Integrals

Mathematics
MATH 1081
Textbook Guide Mathematics: Rational Number, Asymptote, Logarithm

Limits and Derivatives 2.1 The Tangent and Velocity Problems Limits arise when we attempt to find the tangent to a curve or the velocity of an object. 2.2 The Limit of a Function o o It is easy to guess the wrong value if ...

Mathematics
MATH 1081
Textbook Guide Mathematics: Density, Marginal Cost, Hydrostatics

Further Applications of Integration 8.1 Arc Length Arc length o o The length L of C is approximately the length of this polygon and the approximation gets better as we let n increase. o It can be expressed as: If we use Le...

Mathematics
MATH 1081
Textbook Guide Mathematics: Mean Value Theorem, Riemann Sum

Applications of Integrals 6.1 Areas Between Curves We use integrals to find areas of regions that lie between the graphs of two functions. The Riemann sum is an approximation to what we intuitively think of as the area of ...

Mathematics
MATH 1081
Textbook Guide Mathematics: Product Rule, Power Rule, Relative Growth Rate

Differentiation Rules 3.1 Derivatives of Polynomials and Exponential Functions 3.2 The Product and Quotient Rules Dont use the Quotient Rule every time you see a quotient. Sometimes its easier to rewrite a quotient first t...

Mathematics
MATH 1081
Textbook Guide Mathematics: Antiderivative, Inflection, Minimax

Applications of Differentiation 4.1 Maximum and Minimum Values Absolute MaxMin: Local MaxMin: Critical number: o Finding the absolute maxmin: 4.2 The Mean Value Theorem

Mathematics
MATH 1081
Textbook Guide Mathematics: Quadratic Function, Algebraic Function, Function Composition

Functions and Models 1.1 Four ways to represent a function Representations of functions o A function f is a rule that assigns to each element x in a set D exactly one element, called f(x), in a set E. o The set D is called...

Mathematics
MATH 1081

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