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Oswaldo Jiménez

Université Bordeaux I

Biography

I am a mathematician graduated at Central University of Venezuela (1981-1986). At this same University, I got a MSc degree in Mathematics (1986-1989). Then, I got a PhD (Doctorate) in Mechanical Engineering at Université de Bordeaux I, in France (1991-1995). I have worked at the Venezuelan Petroleum Company for almost 15 years (1989-2003), doing applied mathematical and numerical modelling, both for petroleum reservoirs and sedimentary basins. I have also worked for more than 16 years at the University, teaching numerical analysis, differential equations and scientific computing. I have been involved intensively in the mathematical and numerical modelling of porous media phenomena, through the numerical solution of ordinary and partial differential equations, using several numerical methods such as finite differences, finite elements, finite volumes, mimetics, among others. I have also been greatly involved in the process of scientific programming using some computer languages such as C, C++, Fortran, Python, Visual Basic, Matlab, Java, and others. I like solving complex problems by using mathematical, numerical and algorithmic tools.

Education

Phd Mechanical Engineering
Université Bordeaux I
MS Mathematics
Universidad Central de Venezuela
BS Mathematics
Universidad Central de Venezuela

Topics Covered

Functions
Derivatives
Differentiation
Vector Functions
Partial Derivatives
Multiple Integrals
Vector Calculus
Limits
Sequences
Series
Series Tests
Differential Equations
Applications of the Derivative
Integrals
Integration
Integration Techniques
Power Series
Powers and Polynomial
Trig Integrals
Trig Substitution
Matrices
Introduction to Matrices
Taylor Series
Equations and Inequalities
Functions
Linear Functions
Polar Coordinates
An Introduction to Geometry
Introduction to Conic Section
Continuous Functions
The Language of Algebra
Complex Numbers
Exponential and Logarithmic Functions
Quadratic Functions
Polynomials
Rational Functions
Trigonometry
Graphs and Statistics
Parametric Equations
Applications of Integration
Introduction to Trigonometry
Systems of Equations and Inequalities
Algebra Topics That are Reviewed at the Start of the Semester
Functions of Several Variables
Foundations for Geometry
Geometry Basics
Right Triangles
Circles
Introduction to Conic Sections
Introduction to Sequences and Series
Introduction to Combinatorics and Probability
Volume
Vectors

Oswaldo's Textbook Answer Videos

15:13
Calculus: Early Transcendentals

The point $ P(2, -1) $ lies on the curve $ y = 1/(1-x) $.

(a) If $ Q $ is the point $ (x, 1/(1-x)) $, use your calculator to find the slope of the secant line $ PQ $ (correct to six decimal places) for the following values of $ x $:
(i) $ 1.5 $ (ii) $ 1.9 $ (iii) $ 1.99 $ (iv) $ 1.999 $
(v) $ 2.5 $ (vi) $ 2.1 $ (vii) $ 2.01 $ (viii) $ 2.001 $

(b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at $ P(2, -1) $.

(c) Using the slope from part (b), find an equation of the tangent line to the curve at $ P(2, -1) $.

Chapter 2: Limits and Derivatives
Section 1: The Tangent and Velocity Problems
Oswaldo Jiménez
13:09
Calculus: Early Transcendentals

Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct to six decimal places).

$ \displaystyle \lim_{h \to 0}\frac{(2+h)^5 - 32}{h} $,
$ h = \pm 0.5, \pm 0.1, \pm 0.01, \pm 0.001, \pm 0.0001 $

Chapter 2: Limits and Derivatives
Section 2: The Limit of a Function
Oswaldo Jiménez
26:16
Calculus: Early Transcendentals

(a) Evaluate $ h(x) = (\tan x - x)/x^3 $ for $ x $ = 1, 0.5, 0.1, 0.05, 0.01, and 0.005.

(b) Guess the value of $ \displaystyle \lim_{x \to 0}\frac{\tan x - x}{x^3} $.

(c) Evaluate $ h(x) $ for successively smaller values of $ x $ until you finally reach a value of 0 for $ h(x) $. Are you still confident that your guess in part (b) is correct? Explain why you eventually obtained 0 values. (In Section 4.4 a method of evaluating this limit will be explained.)

(d) Graph the function $ h $ in the viewing rectangle $ [-1, 1] $ by $ [0, 1] $. Then zoom in toward the point where the graph crosses the $ y $ -axis to estimate the limit of $ h(x) $ as $ x $ approaches 0. Continue to zoom in until you observe distortions in the graph of $ h $. Compare with the results of part (c).

Chapter 2: Limits and Derivatives
Section 2: The Limit of a Function
Oswaldo Jiménez
14:04
Calculus: Early Transcendentals

Let $ g(x) = \text{sgn}(\sin x) $.

(a) Find each of the following limits or explain why it does not exist.
(i) $ \displaystyle \lim_{x \to 0^+}g(x) $
(ii) $ \displaystyle \lim_{x \to 0^-}g(x) $
(iii) $ \displaystyle \lim_{x \to 0}g(x) $
(iv) $ \displaystyle \lim_{x \to \pi^+}g(x) $
(v) $ \displaystyle \lim_{x \to \pi^-}g(x) $
(vi) $ \displaystyle \lim_{x \to \pi}g(x) $

(b) For which values of $ a $ does $ \displaystyle \lim_{x \to a}g(x) $ not exist?
(c) Sketch a graph of $ g $.

Chapter 2: Limits and Derivatives
Section 3: Calculating Limits Using the Limit Laws
Oswaldo Jiménez
06:45
Calculus: Early Transcendentals

(a) Find a number $ \delta $ such that if $ | x - 2 | < \delta $, then $ | 4x - 8 | < \varepsilon $, where $ \varepsilon = 0.1 $.

(b) Repeat part (a) with $ \varepsilon = 0.01 $.

Chapter 2: Limits and Derivatives
Section 4: The Precise Definition of a Limit
Oswaldo Jiménez
08:05
Calculus: Early Transcendentals

Prove the statement using the $ \varepsilon $, $ \delta $ definition of a limit.

$ \displaystyle \lim_{x \to 4}\frac{x^2 - 2x - 8}{x - 4} = 6 $

Chapter 2: Limits and Derivatives
Section 4: The Precise Definition of a Limit
Oswaldo Jiménez
1 2 3 4 5 ... 186

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