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Calculus I for the Biological Sciences
Simon Fraser University
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Browse the full collection of course materials, past exams, study guides and class notes for MATH 154 - Calculus I for the Biological Sciences at Simon Fraser University verified …

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Yusuf Tuncer

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MATH 154 Lecture 1: MATH 154 D100-Lecture 1- Polynomials and Rational Functions

Math 154 d100- lecture 1-polynomials and rational functions. Power function: a function using the form f(x)=cxn, where c and n are both constants. Exam

MATH 154 Lecture Notes - Lecture 1: Exponentiation, Rational Function, Polynomial

Power function: a function of the form (cid:4666)(cid:1876)(cid:4667)=(cid:1876) where the coefficient (c) and the. 1 can be implied as a coefficient (

MATH 154 Lecture 3: chapter 2

MATH 154 Lecture 3: Domains, Zeroes, & Even/Odd Functions

(cid:3117)(cid:3118) or is not a polynomial, because it does not have an integer exponent. For rational functions, numerator must equal 0 but denominat

MATH 154 Lecture 4: Lecture 3: Function Intersections & Limits

The graphs of 2 functions intersect where the 2 functions are equal to each other. When we cancel x, we assume x 0, or treat x = 0 as a separate case.

MATH 154 Lecture Notes - Lecture 5: Asymptote, Classification Of Discontinuities

A limit is a value you hope to get (may not get that value); very important concept for calculus. A limit at a" exists if & only if both left-hand

MATH 154 Lecture 6: Lecture 5: Limits & Average Rate of Change

When the x-value of a function is large, the leading term dominates the behaviour. So when the x-value is large, we can assume f(x) leading term. If x

MATH 154 Lecture 7: Lecture 6: Limits & Instantaneous Rates of Change/Derivatives

A se(cid:272)a(cid:374)t li(cid:374)e is a li(cid:374)e that (cid:272)rosses 2 spe(cid:272)ifi(cid:272) poi(cid:374)ts o(cid:374) a fu(cid:374)(cid:272

MATH 154 Lecture Notes - Lecture 8: Constant Function

To find the slope of a tangent line, take the derivative as the slope. Recall; the derivative of a function is defined as (cid:4666)(cid:4667)=lim 0(ci

MATH 154 Lecture Notes - Lecture 12: Asymptote, Antiderivative

If there is a limit that is a real number, that is the horizontal asymptote. If a function has a derivative at a point x, it is continuous at x. Some f

MATH 154 Lecture 14: Math 154 D100-Lecture 14-Midterm Exam 1 Solutions (pg 3)

MATH 154 Lecture 14: Math 154 D100-Lecture 14-Midterm Exam 1 Solutions (pg 2)

MATH 154 Lecture 14: Math 154 D100-Lecture 14-Midterm Exam 1 Solutions (pg 1)

MATH 154 Lecture 14: MATH 154 D100-Lecture 14-Midterm Exam 1 Solutions

MATH 154 Lecture 14: Math 154 D100-Lecture 14-Midterm Exam 1 Solutions (pg 4)

MATH 154 Lecture 16: MATH 154 D100- Lecture 16-Sketching Graphs

MATH 154 Lecture 16: Linear Approximation & Newton's Method

With linear approximations, we are guessing based on values that we know. The linearization of a function at a point a is the function given by the tan

MATH 154 Lecture Notes - Lecture 17: Differentiable Function

MATH 154 Lecture Notes - Lecture 17: Second Derivative, Maxima And Minima, Minimax

Math 154 d100-lecture 17-sketching the graph of a function. A function has a local minimum if the value of f (or y) at x0 is smaller than the value of

MATH 154 Lecture 18: MATH 154 D100-Lecture 18-Sketching Graphs

MATH 154 Lecture Notes - Lecture 18: Maxima And Minima

A function f(x) has a local minimum at a point if the value of f at that point is smaller than the value of f at all nearby points. A function f(x) has

MATH 154 Lecture Notes - Lecture 19: Maxima And Minima, Differentiable Function

Global maximum (absolute maximum): the largest/highest point on the graph of a function. Global minimum (absolute minimum): the smallest/lowest point o

MATH 154 Lecture 20: MATH 154 D100-Lecture 20-Optimization

MATH 154 Lecture Notes - Lecture 20: Crop Yield, Maxima And Minima, Logistic Function

MATH 154 Lecture 21: Optimization & Closed Interval Method

MATH 154 Lecture 24: Optimization & Related Rates

If the function cos has derivative sin, find the derivative of cos(x3-2x) Problem: a colony of ants maintains a trail network to connect their nest to

MATH 154 Lecture 25: Related rates problems

If gravel is dumped at 30 ft3/min, that means =(cid:885)(cid:882) We want to know what is when h = 10. If h = r, then we can rearrange the equation so

MATH 154 Lecture Notes - Lecture 26: Product Rule

MATH 154 Lecture Notes - Lecture 27: Implicit Function, Maxima And Minima

1 + 1 + 1 = 3 so the point is on the curve. Note: don"t forget the brackets or you"ll lose marks! With the curve (cid:1876)(cid:2870)+(cid:1876)(cid:18

MATH 154 Lecture 29: Differentiating Exponential Functions & Doubling

Ex and ln(x) are the inverse of each other. For changing to base e, we use the formula (cid:3051)=(cid:1857)ln (cid:4666)(cid:4667)=(cid:1857)ln (cid:4

MATH 154 Lecture Notes - Lecture 31: Exponential Decay, Doubling Time

For this equation, the rate of change of y is proportional to itself. A differential equation is an equation where both sides are functions (functional

MATH 154 Lecture 32: solving differential equations

MATH 154 Lecture 33: Euler's Method & Differential Equation Summary

MATH 154 Lecture Notes - Lecture 34: Slope Field

MATH 154 Lecture Notes - Lecture 35: Radian, Unit Circle, Logistic Function

MATH 154 Lecture Notes - Lecture 36: Inverse Function

MATH 154 Lecture 37: Trigonometry Derivatives

MATH 154 Lecture Notes - Lecture 38: Inverse Trigonometric Functions, Visual Angle, Implicit Function