MTH125-F Fall 2013 Lecture Material

Week 1	Week 2	Week 3	Week 4	Week 5	Week 6	Week 7	Week 8	Week 9	Week 10	Week 11	Week 12

---

Week 12

Date	Topic	Description
12/10/2013	Exam 3 2013 Solutions	Problem 1 (optimization)
		Problem 2 (Newton's method)
		Problem 3 (closed interval method)
		Problem 4 (optimization)
		Problem 5 (L'Hospital's rule)
		Problem 6 (definite integrals)
		Problem 7 (antiderivatives)
		Problem 8 (FTC Version I)
		Problem 9a (mean value theorem)
		Problem 9b (zero derivative theorem)
		Problem 9c (equal derivatives theorem)
		Problem 9d (Fermat's theorem)
		Problem 9e (continuous function theorems)
		Problem 10 (initial value problem)

---

Week 11

Date	Topic	Description
11/25/2013	Exam 3 2012 Solutions	Problem 1 (optimization)
		Problem 2 (Newton's method)
		Problem 3 (closed interval method)
		Problem 4 (optimization)
		Problem 5 (L'Hospital's rule)
		Problem 6 (definite integral)
		Problem 7 (antiderivative)
		Problem 8 (FTC Version 1)
		Problem 9 (derivatives and shapes)
		Problem 10 (initial value problem)
11/25/2013	Exam 3 2010 Solutions	Problem 1 (optimization)
		Problem 2 (Newton's method)
		Problem 3 (closed interval method)
		Problem 4 (optimization)
		Problem 5 (L'Hospital's rule)
		Problem 6 (closed interval method)
		Problem 7a (mean value theorem)
		Problem 7b (Rolle's theorem)
		Problem 7c (zero derivatives theorem)
		Problem 7d (equal derivatives theorem)
		Problem 7e (Fermat's theorem)
		Problem 8 (derivatives and curves)
		Problem 9 (initial value problem)
		Problem 10 (L'Hospital's rule)

---

Week 10

Date	Topic	Description
10/28/2013	The closed interval method	Systematic procedure for finding max and min values
10/28/2013	Critical numbers	Places where a max or min might occur
10/28/2013	Maxima and Minima	Definition of local and absolute maximum and minimum
10/27/2013	The first derivative test	Function behavior at critical numbers
10/27/2013	Concavity	Concavity and tests for it
10/27/2013	Increasing and Decreasing functions	Definition of increasing and decreasing functions

---

Week 9

Date	Topic	Description
10/27/2013	Exam 2 2013 Solutions	Problem 1 (exponential decay)
		Problem 2 (implicit differentiation)
		Problem 3 (tangent line equation)
		Problem 4 (linearization)
		Problem 5 (multilevel chain rule)
		Problem 6 (related rates)
		Problem 7 (linear approximation)
		Problem 8 (derivatives of log and trig functions, chain rule)
		Problem 9 (rates of change)
		Problem 10 (related rates)
10/19/2013	Exam 2 2012 Solutions	Problem 1
		Problem 2
		Problem 3
		Problem 4
		Problem 5
		Problem 6
		Problem 7
		Problem 8
		Problem 9
		Problem 10
10/19/2013	Exam 2 2011 Solutions	Problem 1
		Problem 2
		Problem 3
		Problem 4
		Problem 5
		Problem 6
		Problem 7
		Problem 8
		Problem 9
		Problem 10

Week 8

Date	Topic	Description
10/11/2013	Linearization	The tangent line as linear approximation of the original function
10/11/2013	Differentials	The Liebnitz notation and differentials
10/11/2013	Exponential growth and decay	Exponential models of growth and decay

---

Week 7

Date	Topic	Description
10/11/2013	Section 3.9 Related Rates	Problem 20 (Taylor)
		Problem 19 (Tina)
		Problem 18 (Haela)
		Problem 17 (Anthony)
		Problem 16 (Nicole)
		Problem 14 (Steve)
		Problem 13 (Haela)
		Problem 12 (Anthony)
		Problem 11 (Nicole)
		Problem 10 (Eva)
10/8/2013	Related rates II	Example of related rates
10/8/2013	Related rates I	Example of related rates
10/8/2013	Rates of change II	Example of rates of change
10/8/2013	Rates of change I	Example of rates of change
10/6/2013	Logarithmic differentiation	A differentiation technique useful for complicated products and quotients
10/6/2013	Hyperbolic functions	Like the trig functions, but based on the geometry of a hyperbola instead of a circle

---

Week 6

Date	Topic	Description
10/5/2013	Implicit differentiation	Derivatives of functions that are not explicitly defined
10/5/2013	Liebnitz notation form of the chain rule	The chain rule expressed in Liebnitz notation
10/5/2013	Derivative of logarithms with arbitrary bases	The derivative of loga(x)
10/5/2013	Derivative of the natural logarithm	The derivative of ln(x)
10/5/2013	Higher order chain rule	Chain rule with more than two levels of function composition
9/29/2013	The chain rule	Derivatives of function compositions
9/29/2013	Trig functions	Derivatives of trigonometric functions
9/29/2013	The quotient rule	Derivatives of quotients
9/29/2013	The product rule	Derivatives of products
9/29/2013	Common derivatives	Powers, sums, differences, constant multiples, and exponentials

---

Week 5

Date	Topic	Description
9/28/2013	Fall 2013 Exam I Solutions	Solutions for the 9/27/2013 Calculus I exam.
9/28/2013	Curve algorithm	How curve for exam scores is calculated.
9/25/2013	Exam I Solutions V1	Solutions for problems 1-7 for prior year's first exam.
9/23/2013	Exam I Solutions V2	Solutions for problems 1-7 for prior year's first exam.
9/23/2013	Example Using the Precise Definition of a Limit at Infinity	An example of how to apply the precise definition of a limit at infinity.
9/23/2013	Limits at Infinity	Function limits as x approaches infinity or negative infinity.
9/23/2013	Proof that differentiability implies continuity	Note that continuity DOES NOT imply differentiability; the converse is false.
9/23/2013	The Intermediate Value Theorem	The intermediate value theorem guarantees that a continuous function assumes every value in a certain range.
9/22/2013	Higher Derivatives and Liebnitz notation	Definition of the second and higher derivatives; Position, velocity, and acceleration; Liebnitz notation for derivatives.
9/22/2013	Position and Velocity	Calculating the average and instantaneous velocity

---

Week 4

51d08532-55fe-4510-bf6a-f89f7527c477

Date	Topic	Description
9/21/2013	Friday Open Mic Volunteers presenting problem solutions for 10 participation points	Section 2.7 Problem 4a (Christopher)
		Section 2.7 Problem 5 (Christina)
		Section 2.7 Problem 4a (Anthony L)(Sorry, most of video was chopped off, but you can see some of the conclusion)
9/19/2013	Simplification with conjugates	Using the identity (a+b)^2=(a+b)(a-b) to simplify difference quotients.
9/18/2013	Left and rightcontinuity	Definition and examples of left and right hand limits and continuity.
9/17/2013	Derivative example 2	Calculating the derivative of 1/x from the definition
9/17/2013	Derivative example 1	Calculating the derivative from the definition.

---

Week 3

Date	Topic	Description
9/13/2013	Precise definition of a limit example	Example using the precise definition to prove that the limit of a function has a specified value.
	The Precise Definition of a limit	The "real" definition of a limit of a function using epsilons and deltas.
9/12/2013	Constant multiples	Limits of functions defined as a constant times another function.
	The Squeeze theorem	Theorem for limit of a function "squeezed" between two others.
	Tangent line example - x cubed	Computing the slope of the tangent line for f(x)=x cubed
	Tangent line example - 1/x	Computing the slope of the tangent for f(x)=1/x
	Tangent example 1	Example of computing the slope of the tangent line
	Tangent example 2	Example of computing the slope of a tangent line
	Sums and differences	Limits of functions defined as sums or differences of other functions.
	Products and quotients	Limits of functions defined as products or quotients of other functions.
	Nearly identical functions	Theorem on limit of two functions that differ at a single point.
	Continuous functions	Limits of continuous functions on their domains by direct substitution.
	Infinite limits	Limits where the function value approaches infinity or -infinity as x approaches a.
	One-sided limits	Limits where x approaches a from one side only.
	Deinition of a limit (imprecise)	The more intuitive but less precise definition of a limit

Week 2

Date	Topic	Description
9/6/2013	Friday Open Mic Volunteers presenting problem solutions for 10 participation points	Section 1.6 Problem 36a (Nicole) (With apolgies for my finger over the camera lens.....)
		Section 1.6 Problem 35a (Taylor)
		Section 1.6 Problem 38a (Steven)
		Section 1.3 Problem 34 (Haela)
		Section 1.1 Problem 35 (Tyler) (remarks)
		Section 1.6 Problem 52a (Patrick)
		Section 1.1 Problem 34 (Christ)
		Section 1.6 Problem 38b (Omayra)
9/2/2013	Function composition	Creating a new function as the composition f(g(x)) of two existing functions.
9/2/2013	Combining functions arithmetically	Defining a new function as the sum, difference, product, or quotient of two functions.

---

---

Week 1

Date	Topic	Description
9/1/2013	Power functions	Review of power functions (powers and roots) and their basic properties.
9/1/2013	Trigonometric functions	Review of trigonometric functions and their basic properties.
9/1/2013	Rational functions	Review of rational functions (functions of the form P(x)/Q(x), where P and Q are polynomials).
9/1/2013	Polynomials	Review of the properties of polynomials and the fundamental theorem of algebra, which states that every polynomial of degree n has exactly n roots counting complex roots and multiplicities.
9/1/2013	Secant lines, difference quotients, and average rates of change	Definition of the secant line and difference quotient and the average rate of change of a function on an interval.
8/31/2013	Linear functions	Review of the properties of linear functions, point-slope formula, inverses of linear functions.
8/31/2013	Function evaluation: f(x+h)-f(x) forms	Overview of evaluation of function differences.

---

Back to Dr. Quinn's home page
Back to Stonehill Math Department web page
Back to Stonehill main page